A Multi-Objective Tri-Level Algorithm for Hub-and-Spoke Network in Short Sea Shipping Transportation

Hub-and-Spoke (H&S) network modeling is a form of transport topology optimization in which network joins are connected through intermediate hub nodes. The Short Sea Shipping (SSS) problem aims to efficiently disperse passenger flows involving multiple vessel routes and intermediary hubs through which passengers are transferred to their final destination. The problem contains elements of the Hub-and-Spoke and Travelling Salesman, with different levels of passenger flows among islands, making it more demanding than the typical H&S one, as the hub selection within nodes and the shortest routes among islands are internal optimization goals. This work introduces a multi-objective tri-level optimization algorithm for the General Network of Short Sea Shipping (GNSSS) problem to reduce travel distances and transportation costs while improving travel quality and user satisfaction, mainly by minimizing passenger hours spent on board. The analysis is performed at three levels of decisions: (a) the hub node assignment, (b) the island-to-line assignment, and (c) the island service sequence within each line. Due to the magnitude and complexity of the problem, a genetic algorithm is employed for the implementation. The algorithm performance has been tested and evaluated through several real and simulated case studies of different sizes and operational scenarios. The results indicate that the algorithm provides rational solutions in accordance with the desired sub-objectives. The multi-objective consideration leads to solutions that are quite scattered in the solution space, indicating the necessity of employing formal optimization methods. Typical Pareto diagrams present non-dominated solutions varying at a range of 30 percent in terms of the total distance traveled and more than 50 percent in relation to the cumulative passenger hours. Evaluation results further indicate satisfactory algorithm performance in terms of result stability (repeatability) and computational time requirements. In conclusion, the work provides a tool for assisting network operation and transport planning decisions by shipping companies in the directions of cost reduction and traveler service upgrade. In addition, the model can be adapted to other applications in transportation and in the supply chain.