## 5 Case Study Applications
As anticipated, the proposed solutions in every case develop the routes in geographically separated sub-regions (northern and southern islands). The results in Figure 9 indicate that C2a provides the shortest vessel routes in total, C2b the minimum cumulative passenger-hour solution, and C2c a more comprehensive solution that aims to facilitate both objectives. In general, the lattecompetitive figures in total vessel traveling distance and time as well as in cumulative passenger time spent on board. Compared to case C1, the total distance has marginally been extended, but the passenger hours have been sizably cut down. In scenario C3, one vessel departs from Piraeus central port and another from a hub node, the latter being alternatively set in one of three large islands (Chios, Limnos, or Ikaria) that can serve as hub connectors. Three solutions have been developed corresponding to each of the alternative connectors (C3a, C3b, C3c). A fourth case strives for an optimal solution by demanding the algorithm to automatically assign the hub node among the three islands (C3d). The evaluation is made upon trade-off solutions including the total vessel route distance (D) and the cumulative passenger time (PH), with indicative results presented in Figure 10. All solutions present comparable traveling distance values (within a 4% deviation range), while C3c outperforms in terms of passenger time. This is because Ikaria is closer to Piraeus port and in the core of the islands with high travel demand. In C3d, the algorithm has selected Chios as a hub and provided a competitive solution even though the algorithm complexity rises significantly in the case that the algorithm needs to determine the hub-node location internally. This capability may be highly effective in large-scale problems or sparsely positioned island nodes. In the latter case, a full algorithm implementation can initially provide almost-best hub node selection, while a downgraded algorithm application (with known hubs) can provide improved routing solutions. In a broader problem structure, case C4 considers up to two ships departing from central ports (Piraeus and Rafina) and one from a hub node to be assigned by the model among Chios, Limnos, or Ikaria islands. When optimizing the total traveling distance (C4a), the model proposes a solution involving one vessel from Piraeus Central Port, covering the southern part of the islands, and another from the hub node of Chios with a northern direction. Although reducing the total traveling distance, the employment of two vessels results in high passenger hours spent on board and extensive trip times. Optimizing the total passenger hours on board (C4b) leads to a three-vessel solution with almost half the total passenger and individual trip time (in comparison to C4a), at the expense, however, of the total traveling distance, which increases by a factor of approximately 25% (Figure 11). The multi-objective approach (C4c) provides a balanced solution in terms of  
Figure 9: Optimization results for case study C2 (two vessels from central ports) (the colours in the numbers below correspond to those of the lines in the maps). (a) C2a: D\({}_{1}\)/D\({}_{2}\)/D\({}_{\text{tot}}\) = 315/339/654 nm, T\({}_{1}\)/T\({}_{2}\)/T\({}_{\text{tot}}\) = 13:00/13:23/26:23 h, PH = 12,265 h, T\({}_{\text{max-trip}}\) = 13:23 h. (b) C2b: D\({}_{1}\)/D\({}_{2}\)/D\({}_{\text{tot}}\) =370/421/791 nm, T\({}_{1}\)/T\({}_{2}\)/T\({}_{\text{tot}}\) = 14:52/16:35/31:27 h, PH = 10,369 h, T\({}_{\text{max-trip}}\) = 16:35 h. (c) C2c:D\({}_{1}\)/D\({}_{2}\)/D\({}_{\text{tot}}\) =427/231/658 nm, T\({}_{1}\)/T\({}_{2}\)/T\({}_{\text{tot}}\) =17:08/9:23/26:31 h, PH = 10,732 h, T\({}_{\text{max-trip}}\) = 17:08 h.  
traveling distance and total passenger hours (with three vessels in operation). However, the generated solution is not entirely satisfactory in terms of the max trip time (26:16 h), which results from the fact that a slow-speed vessel has been assigned to serve the distant islands.