## 4 Results
### Preliminary Optimizations  
Some preliminary optimizations of the overall instance have been performed by X-Press, using the ranges of the parameters and the penalty coefficients shown in Table 3, in order to identify the ranges of the choice variables to be considered in the multi-objective optimization. In this preliminary optimizations the objective function is the minimum value of _OBJFun_, Equation (44), for the summer cruise. The preliminary results have been obtained by setting the gap at 1% of the current value of the objective function. They show that, with the penalty coefficients considered, neither the photovoltaic panels nor the solar thermal collectors are included in the optimal solution. The same happens if the penalties are reduced by 4 times, showing that, for the conditions considered, these components can be excluded. In particular, the solar thermal collectors do not appear in the optimal solution even by adopting these extremely low values of the corresponding penalty factor, indicating how their contribution to the production of thermal energy is actually nullified by the wide availability of heat on board and by the high value of efficiency of the integration boilers. Table 4 shows some of the results obtained by optimizing the instance with Xpress, varying the maximum number of Stirling groups that can be present in the optimal solutions, the maximum number of ORC groups and the maximum value of the flow exchanged with the HTW storage. One or more ORC groups and several Stirling groups are generally included in the optimal solution together with the absorption chillers, having a total installed cooling capacity of 8000 kW. Furthermore, with the adopted values of the penalty coefficients, the tension to carry out an important energy recovery by means of Stirling groups is much greater than the tension to introduce ORC groups. In Table 4, the optimizations which give the maximum allowed number of Stirling groups as optimal results are highlighted in yellow. The results reported in the second part of Table 4 show very limited variations in the total fuel consumption as the maximum allowed number of ORC groups increase. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & **Ref. Value** & \multirow{2}{*}{**Units**} & **Penalty** & **Penalty Ref.** \\  & **or Range** & & **Function** & **Value or Range** \\ \hline
**Max number of Stirling** & 10–40 & - & _PEN\_str_ & 1 & [10 m\({}^{3}\)] \\
**Max number of ORC** & 10–25 & - & _PEN\_orc_ & 1 & [10 m\({}^{3}\)] \\
**COP\_abs** & 0,60 & - & - & - & - \\
**Pel\_strsup** & 50 & [kW] & - & - & - \\
**Pel\_orcsup** & 150 & [kW] & - & - & - \\
**Cool\_abs\_max** & 10 & [MW] & _PENabs_ & 1/360 & [10 m\({}^{3}\)/kW] \\
**Int\_HTW\_max** & 10 & [MW] & - & - & - \\
**Input/Output\_HTW\_Max** & 1–7 & [MW] & _PEN\_HTW_ & 0.002 & [10 m\({}^{3}\)/kW] \\
**ApvMax** & 1000 & [m\({}^{2}\)] & _PENpv_ & 1/80–1/320 & [10 m\({}^{3}\)/m\({}^{2}\)] \\
**AstMax** & 500 & [m\({}^{2}\)] & _PENst_ & 1/50–1/200 & [10 m\({}^{3}\)/m\({}^{2}\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main design variables, with their variation ranges and penalty coefficients.