## 4 Results
### Pareto Front of the Bi-Level Optimization  
On the basis of the preliminary optimization, the bi-level optimization was carried out according to the procedures presented in Chapter 3. The multi-objective optimization carried out with modeFRONTIER(r) allowed to identify the Pareto front for the two cases examined (winter and summer cruise). The optimal values identified by the solutions on the Pareto front (Figures 11 and 12) are within the defined ranges and do not show a particular tension towards the upper or lower limits of the ranges, with the exception of the size of the HTW thermal storage in the summer case, whose optimal values tend to stay close to the upper limit of the interval (a peak of the probability density function can be seen in the diagonal of the scattering matrix, Figure 14). Therefore, some extensions of the ranges considered are not expected to improve the solutions on the front. The different assumptions about the summer and winter reference cruises entail a clear difference in the optimized solutions of the energy recovery system. In particular, the absence of a refrigeration load during the winter cruise makes the absorption chiller useless (and always leaves the compression chiller unused), freeing the thermal power for the operation of the ORC groups, which receive energy from the same thermal carrier (hot water at about 90 \({}^{\circ}\)C). In the summer cruise, the using of the absorption chiller is more convenient than the compression one, taking into account the considered efficiency (\(CO\_abs=0.60\); \(CO\_com=4.00\); \(eta\_orc=0.07\)), so that the number of ORC groups of 150 kW, installed in the solutions on the Pareto front, is reduced to one, or none. Figures 11 and 12 show the Pareto front for the summer and winter cases, respectively; the red circle indicates the most interesting solutions from the point of view of reducing consumption. In fact, with reference to the designs considered, it is not advantageous to accept higher penalties because the overall consumption does not drop further, as instead happens in the range 64-88 penalty points for the summer case and in the range 86-112 penalty points for the winter case. Table 6 shows the values of the main choice variables for the two compromise solutions identified. As can be seen, in the summer case there is an important thermal accumulation, favored by the high value allowed for the thermal flow exchanged with the storage (7000 kW), while there are no ORC groups. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Cruise** & **Summer** & **Winter** \\ \hline
**Range of Stirling groups** & 15–20 & 12–20 \\
**Range of ORC groups** & 0–3 & 6–12 \\
**Solar panel area \(App\) [m\({}^{2}\)]** & zero & zero \\
**Solar thermal collector area \(Ast\) [m\({}^{2}\)]** & zero & zero \\
**Absorption chiller size, \(Cool\_abs\_size\) [kW]** & 7–8000 & zero \\
**Compression chiller size, \(Cool\_com\_size\) [kW]** & 2000 & 2000 \\
**Steam storage size, \(Lev\_St\_size\) [kWh]** & zero & zero \\
**HTW storage size \(Lev\_HTW\_size\) [kWh]** & 15–25,000 & 30–50,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ranges for the optimization variables managed by the external level. Figure 11: Pareto front of the optimal solutions in the summer case. The red circle indicates the most interesting solutions from the point of view of reducing consumption. Figure 12: Pareto front of the optimal solutions in the winter case. The red circle indicates the most interesting solutions from the point of view of reducing consumption. This consideration leads to take into account the solutions in the area where the slope of the front changes and the number of Stirling groups is close (or coincident) to the lower limit of the interval considered. Consequently, the solution deemed most interesting in the winter case is the ID 210, indicated on the Pareto front with the red circle and shown in Table 6.  
Figure 14 shows the scattering matrix of the solutions analyzed for the summer case.