## 5 Results and Discussion
Furthermore, Figure 5 shows that the total cost of maximizing the PCR is minimized using ISA algorithm less than the total cost by using GA.  
Table 4 shows the optimal maintenance plan to attain acceptable performance within the available annual maintenance budget ($80,000). Therefore, the maintenance activities are distributed for all 49 sections for 3 years. For the first year t = 1 and for Sana'a road that contains 10 sections (from 1 to 10), sections 2, 6, 5, and 10 are not maintained M-00 (blue colored). However, sections 1, 4, 7, 8, and 9 are maintained by the maintenance activity M-01 (yellow colored), and Section 3 is maintained by using M-02 (green colored). In the second year, sections 1 and 3 are not maintained (M-00). However, sections 2, 5, 8, and 9 are maintained by using M-01, and sections 4, 6, 7, and 10 are maintained by using M-02.  
Figure 4: Convergence of the cumulative PCR for 3 years and 49 sections.  
Figure 5: Convergence of the cumulative maintenance cost for 3 years and 49 sections.  
Finally, in the third year, sections 2, 3, 4, and 7 are not maintained. However, sections 1, 5, 6, 8, 9, and 10 are maintained by using M-01. The last column in Table 4 shows that the PCR of about 36 sections improved to rank 4. However, 13 sections still need maintenance, which can be maintained in the third year because the total cost is low this year.  
Figure 6 shows how the PCR is maximized by 193% from 1.22 in 2019 to 3.59 in 2022. The PCR maximization is constrained with the predefined annual budget ($80,000) and $240,000 for three years. Also, Figure 7 shows the annual maintenance cost for three years scheduled maintenance, where the average cost of three years is $56,515,446. Table 5 displays the obtained optimal total cost using the ISA algorithm is $169,546.34, where the cost-saving is about 29.4%. However, the total cost using GA is about $178,000, which is higher than the cost by using ISA. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Section** & \multicolumn{3}{c}{**Input Variables of ISA Algorithm**} & **Section** & \multicolumn{3}{c}{**Input Variables of ISA Algorithm**} \\ \hline
**s** & \(\mathbf{X_{MA}(s,\,t=1)}\) & \(\mathbf{X_{MA}(s,\,t=2)}\) & \(\mathbf{X_{MA}(s,\,t=3)}\) & **s** & \(\mathbf{X_{MA}(s,\,t=1)}\) & \(\mathbf{X_{MA}(s,\,t=2)}\) & \(\mathbf{X_{MA}(s,\,t=3)}\) \\ \hline  
& & \\ \hline \end{tabular}
\end{table} 
Table 4: Optimal maintenance activity plan by ISA algorithm to improve the pavement condition. Furthermore, the effectiveness of the results is statistically analyzed using the range and standard deviation of the PCR of the maintained roads in each year as depicted in Figure 8. Where the standard deviation and PCR range are decreasing with the planned annual maintenance. Moreover, the ISA algorithm utilized the maintenance activity M-01 about 21%, however, M-04 used rarely -1% as depicted in Figure 9. These results reveal that the pavement maintenance of case study can be done effectively with the lowest cost. In addition, Figure 10 shows that the maintenance activities are optimally distributed between road classes. For the arterial roads, M-01 is the most used maintenance activity, however M-04 is never used. For local access roads, all maintenance activities are used, where M-02 is mostly used. For the main roads, all maintenance activities are applied, where the M-01 is mostly used. These results prove the effectiveness of the proposed optimization method for lowest cost of pavement maintenance management. Figure 6: Improvement of PCR. Figure 7: Annual maintenance cost during three years. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Year** & \(t=0\) & \(t=1\) & \(t=2\) & \(t=3\) & **Sum of \(t=1,2,3\)** \\ \hline Total annual PCR & 60 & 128 & 166 & 176 & 470 \\ Average annual PCR & 1.22 & 2.61 & 3.39 & 3.59 & 9.59 \\ Annual cost (\$) & – & 78,272.06 & 70,650.90 & 20,623.38 & 169,546.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Total annual PCR and its maintenance cost. Figure 8: Range and standard deviation of PCR.