## 5 Discussion  
In this study, a regression model and multi-objective optimization were focused on achieving the goal of finding significant factors and optimal parameters for desirable responses. The regression equations for each TPMS cell type provide insights into the influence of lattice thickness and cell size on the surface area to volume ratio (SA/V\({}_{\text{S}}\)) and temperature difference (\(\Delta\)T). From a practical standpoint, these models allow designers to predict the impact of design modifications without conducting additional simulations. For instance, if minimizing \(\Delta\)T is prioritized due to energy constraints, the model suggests increasing lattice thickness while keeping cell size moderate. Conversely, if maximizing SA/V\({}_{\text{S}}\) is the goal, thinner lattice structures should be used. For example, the regression model for the Schwartz structure reveals that both lattice thickness and cell size significantly impact SA/V\({}_{\text{S}}\) and \(\Delta\)T, whereas for other structures, lattice thickness is the dominant factor. This suggests that Schwartz structures offer more tunability, making them suitable for scenarios where both objectives are equally important. The main effect plots and Pareto charts from Tables 3 and 4 support these findings. In Table 5, optimal parameters were calculated in Minitab by providing 75%, 50%, and 25% response. Having SA/Vs = 0.75; \(\Delta\)T = 0.25 means that maximizing SA/Vs was given 3 times more importance than minimizing \(\Delta\)T and vice versa for SA/Vs = 0.25; \(\Delta\)T = 0.75. For SA/Vs = 0.5; \(\Delta\)T = 0.5, both objectives were given equal importance. By using this analysis, factor values are predicted that bring out the best possible multi-objective outcome of the desired balance for this study. Depending on the conditions, any of these settings--or any value between 0% and 100%--can represent the overall optimum. For instance, factors such as geometry with high manufacturing costs or fluctuations in energy prices for temperature reduction may shift the priority of these objectives, leading to a higher weight for one over the other. * When SA/V\({}_{\text{S}}\) is given higher priority (0.75 weight), the optimization process favors thinner lattice structures and smaller cell sizes to maximize surface area for condensation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Cell Type** & \multicolumn{4}{c}{**SA/V\({}_{\text{S}}\)**} & \multicolumn{4}{c}{**\(\Delta\)T**} \\ \cline{2-9}  & **S** & **R\({}^{2}\)** & **Adjusted R\({}^{2}\)** & **Predicted R\({}^{2}\)** & **S** & **R\({}^{2}\)** & **Adjusted R\({}^{2}\)** & **Predicted R\({}^{2}\)** \\ \hline \hline Gyroid & 0.09 & 97.63 & 96.20 & 93.76 & 0.13 & 97.11 & 95.38 & 93.26 \\ \hline Diamond & 0.10 & 97.69 & 96.31 & 94.27 & 0.15 & 96.22 & 93.95 & 90.04 \\ \hline Lidinoid & 0.12 & 96.76 & 94.81 & 91.45 & 0.08 & 96.58 & 94.52 & 89.66 \\ \hline SplitP & 0.13 & 97.63 & 96.21 & 93.71 & 0.20 & 95.69 & 93.11 & 90.06 \\ \hline Schwartz & 0.05 & 98.11 & 96.98 & 94.78 & 0.07 & 98.50 & 97.60 & 93.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Model summary listing S, R\({}^{2}\), Adjusted R\({}^{2}\), and Predicted R\({}^{2}\) of each response for each cell type, showing the models fit the data well. When \(\Delta\)T is prioritized (0.75 weight), the model selects thicker lattice structures, which enhance heat transfer and reduce the temperature difference. * At equal weighting (0.5, 0.5), the optimization finds a balanced solution that moderately enhances both objectives. * These findings are important for considering design decisions:
* Minimizing \(\Delta\)T is critical to reduce cooling loads that will lead to energy efficient solutions. Hence, thicker lattice structures should be chosen. * To increase water collection efficiency, condensation surface area must be maximized. Hence, thinner structures should be prioritized.