## 3 Results and Discussions
### Optimization Model  
The optimization models \(P1\) and \(P2\) require estimating the total cost \(F_{i}\) for microgrid to construct and operate in a specific location \(Geo_{i}\). HOMER design software [34] was used to determine the cost of a 4 MW microgrid consisting of a mix of diesel generators, DC/AC converters, flat panel photovoltaic cells, 1.5 kW wind turbines, and 1 kW lithium acid batteries for storage. Furthermore, the cost of real estate assuming a greenfield deployment of the microgrid was estimated for each \(Geo_{i}\) Considering a lifetime of 23 years and a net present cost value of \(F_{i}\) covering the capital cost, replacement, salvage, operating and fuel, and repair, a discount value of 6% was found as \(F_{i}=\{6,6.2,7.4,7.2,11,11.5,5.4,5.6,4.4\}\). The difference in \(F_{i}\) values is the real estate cost. The additional \(P1\) optimization model \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**eNB ID** & \begin{tabular}{c} **Coverage** \\ **Index** \\ \end{tabular} & \
\begin{tabular}{c} **Population** \\ **Covered** \\ \end{tabular} &
\begin{tabular}{c} **Power Consumption** \\ **(kWh)** \\ \end{tabular} & \(TWV_{SI}\) \\ \hline
780032 & 1 & 2688 & 15 & \(-\)3.079 \\
780540 & 3 & 5948 & 25 & 2.425 \\
780167 & 2 & 4593 & 20 & \(-\)0.277 \\
780477 & 2 & 4593 & 20 & \(-\)0.277 \\
780169 & 1 & 3316 & 15 & \(-\)2.965 \\
780218 & 1 & 6078 & 15 & \(-\)2.460 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Facility** & \begin{tabular}{c} **Power Consumption** \\ **(kWh)** \\ \end{tabular} & \begin{tabular}{c} **Size** \\ **(kWh)** \\ \end{tabular} & \
\begin{tabular}{c} **Occupancy** \\ \end{tabular} &
\begin{tabular}{c} \(TWV_{SI}\) \\ \end{tabular} \\ \hline Petersen Center & 224,000 & 16,000 & 12,508 & \(-\)0.198 \\ PPG Paints Arena & 10,080,000 & 720,000 & 19,758 & \(-\)0.017 \\ Convention Center & 21,000,000 & 1,500,000 & 109,445 & 2.225 \\ Irish Centre & 168,000 & 12,000 & 315 & \(-\)0.503 \\ Sigmas Center & 140,000 & 10,000 & 150 & \(-\)0.507 \\ Sherwood Center & 252,000 & 18,000 & 500 & \(-\)0.499 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Emergency shelter. variables were \(S_{i}=4 MW\)\(\forall i\) and \(\alpha=\beta=0.5\). Table 10 shows the outcomes of solving optimization model \(P1\) and the heuristic based on \(TI_{i}\) while varying the number of sequentially built microgrids. Table 10 clearly shows that \(Geo_{5}\) is the preferred location for a microgrid due to the high number of critical nodes in that geographic space. Furthermore, Table 10 shows that both the optimization model and heuristic implemented sequentially favor the critical squares with high total weight value, even in the case of multiple microgrids. The trade-offs were also investigated through the infrastructure and cost weight by modifying the value of \(\alpha\) and the value of \(\beta\) considering one microgrid, with the results presented in Table 11. The table shows that geographical zone number five is again selected, excluding the case where \(\alpha=0\) shows that the cost is only minimized. \begin{table}
\begin{tabular}{c c c c} \hline
**Microgrid Quantity** & **1** & **2** & **3** \\ \hline Heuristic \(Geo_{i}\) & 5 & 5, 5 & 5, 6 \\ \(P1\) Optimization Model \(Geo_{i}\) & 5 & 5, 5 & 5, 6 \\ \hline \end{tabular}
\end{table} 
Table 10: Optimization vs. Heuristic represented by square numbers. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(Geo_{i}\) & **Healthcare** & **Water** & **Cellular** & **Shelter** & **TI** & **Rank** \\ \hline
1 & 0.5793 & 0.5598 & 0 & 1.1171 & 2.2562 & 5 \\
2 & 0 & 0 & 0 & 0.0527 & 0.0527 & 8 \\
3 & 0.3497 & 1 & 3.0117 & 0 & 4.3614 & 3 \\
4 & 0 & 0 & 0 & 0 & 0 & 9 \\
5 & 8.7257 & 0 & 3.5511 & 4.0278 & 16.3046 & 1 \\
6 & 3.2216 & 0 & 4.3177 & 0.1063 & 7.6456 & 2 \\
7 & 0.5609 & 0 & 0 & 0 & 0.5609 & 7 \\
8 & 0 & 0 & 1.2411 & 0 & 1.2411 & 6 \\
9 & 0 & 0.0107 & 2.9535 & 0 & 2.9642 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Total importance value for every zone.