## 1 Introduction  
Hub-and-Spoke (H&S) network modeling is a special case of the vehicle routing problem (VRP), which refers to determining the most efficient routes of various types of fleets for moving passengers and cargo. This problem is widely applied in numerous fields of operational research, such as transportation, telecommunications, and logistics. In conventional \"Point to Point (P2P) transit\" systems, vehicles travel directly from each node to any other. In contrast, a Hub-and-Spoke network system is an alternative route-planning method consisting of primary nodes and peripheral radial connections. This structure is referred to as a series of \"spokes\" that connect outlying points to a central hub. The H&S structure is the dominant transportation practice nowadays as it provides several benefits, including reduced route lengths and transit times, effective use of fleet assets, comfortable journeys for travelers, and a lower carbon footprint due to reduced fuel consumption and emissions.  
The H&S model was first introduced by Delta Airlines in 1955 at the Atlanta airport to compete with Eastern Air Lines. In this innovative (in those days) system, airplane routes were planned to carry passengers to Delta's hub airport in Atlanta, connecting them to other Delta flights. After the Airline Deregulation Act in 1978, several other airlines adopted Delta's H&S structure. Later, distribution and logistics companies successfully implemented the H&S model to gain a competitive business advantage. They found that this method reduces transportation costs and inventories while improving delivery cycle times. Nowadays, the H&S model is widely applied to other transportation systems such as sea shipping, freight rail transport, industrial distribution, telecommunications, etc.  
Short Sea Shipping (SSS) route planning is a field in transportation to which H&S modeling can be applied. SSS is the maritime transport of passengers and goods over relatively short distances, as opposed to intercontinental cross-ocean deep-sea shipping. According to the EU (COM1999 317 final) [1], SSS is defined as \"the movement of cargo and passengers by sea, between ports situated in geographical Europe or between those ports and ports situated in non-European countries having a coastline on the enclosed seas bordering.\" SSS is promoted within the European Union in the framework of sustainable and safe mobility as it is much more energy efficient and relatively safer compared to other transport modes. Additionally, SSS strengthens community cohesion, facilitating connections between the Member States and European regions and, along with other modern trends such as autonomous technologies [2], increases transport efficiency to meet current and future demands arising from economic growth.  
Most existing research efforts target logistics and aviation-related applications and focus mostly on economic parameters, approaching the problem from the operator's perspective of increasing profitability. The present study considers the problem from a more global perspective and within a more generalized framework, in which additional parameters are considered related to passenger hours spent on board, individually or cumulatively. In addition, several constraints and preferences (technical, operational, or comfortability-related) are included to make the problem as practical as possible. The research study aims at developing a multi-objective tri-level optimization model for optimizing the H&S network operation adopted within the General Network of Short Sea Shipping (GNSSS) needs.