## 6 Conclusions  
The Short Sea Shipping (SSS) problem for passenger transport involves multiple vessel routes originating at a central port or at intermediary hubs through which passengers are transferred to their final destination. The problem formulation contains elements of the Hub-and-Spoke and Travelling Salesman structures, 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. Considering, in addition, that the passenger flows change along route nodes, the use of formal optimization seems rather imperative to provide efficient routing solutions. This work introduces a multi-objective trilevel optimization algorithm for the passengers' Short Sea Shipping (SSS) problem, incorporating economic and non-economic considerations. Besides the travel cost associated with the travel distance, the cumulative passenger hours spent on board, the trip time for each passenger, the vessel route length, and related constraints or preferences (e.g., service priority of specific islands) are considered to make the model as applicable to actual practice as possible. The optimization outcome refers to the selection of hubs, the island groups that are served by each line, and the corresponding service sequence. The mathematical formulation of the optimization model has been structured in the form of matrix computations to simplify the internal calculations and minimize the oversights in algorithm implementation. The algorithm efficiency is demonstrated through several case studies of variable size and operational scenarios based on a Short Sea Shipping network of the Aegean Sea (Greece) and their connection with the mainland. The results indicate that the algorithm provides rational and stable (repeatable) solutions in accordance with the desired objective, the decision parameters and problem constraints. In particular, when the total distance is to be minimized, the algorithm attempts to geographically divide the service region and accordingly allocate the vessel routes within each region on the basis of the minimum travel length. If the main objective is the minimization of the cumulative passenger hours on board, islands with heavier traveler flows tend to be served in priority and with high-speed vessels while islands with light flows are facilitated via intermediate hub nodes and smaller ferries. The multi-objective consideration leads to solutions that are quite scattered in the solution space, indicating the necessity of employing formal optimization methods. In particular, the solution range in a typical Pareto diagram presents a variation in terms of the distance traveled in the order of 30 percent and more than 50 percent in relation to the cumulative passenger hours. Evaluation results further indicate a satisfactory algorithm performance in terms of result stability and computational time requirements. More specifically, for small-sized problems, the algorithm convergence in general to the same optimum solution in less than a few minutes. In larger-scale cases, the results are adequately repeatable (all independent runs converge within 2% away from the best-found values) while the computation time is in the order of 20 to 60 min. Besides the application to the heavy passenger traffic of Greek islands, the proposed formulation can also be applied in other island regions of the world, such as the Caribbean, Indonesia, or the Baltic Sea. These networks have increased complexity, including densely populated islands, sovereignty scattering across many nations, and dependencies that may raise particular constraints and additional challenges in implementation. Furthermore, although the algorithm focuses on passenger transportation, it presents sufficient flexibility to facilitate cargo transportation in similar cases. The proposed model is a special case of the H&S problem with emphasis on island clusters that are served partly sequentially and partly through intermediate hubs.