**4. Case Study**

The applicability of proposed algorithm was demonstrated by performing a case study. The data of the case study was obtained from the General Corporation of Roads and Bridges, Hajjah, Yemen, which is classified as a developing country. Roadway network contains 16 roads comprises arterial, main, and local access roads; which include 49 sections with 23 km total length. Code, length, width, and initial PCR for each road section are

presented in Table 3. Annually, the maintenance activities are implemented within a specified available budget of around \$80,000 based on the agency constraints. This study adopts a medium-term planning time horizon of three-year (2020–2022) to develop the pavement maintenance program. Maintenance costs related to repair decisions were collected from the General Corporation of Roads and Bridges in Yemen as 0.6, 1.08, 2.09, and 3 (\$/m2) for crack seal, slurry seal, thin asphalt overlay, and thick asphalt overlay, respectively.



#### **5. Results and Discussion**

The ISA and GA algorithms are applied to maximize the total PCR of all road sections for three years and, at the same time, minimize the total cost of pavement maintenance. The PMMS model and ISA and GA algorithms are coded using MATLAB 2019b. The

population size of both algorithms is set to 100, and the maximum number of iterations is set to 10,000. Therefore, the number of function evaluations is 100 × 10,000 = 1,000,000. The optimization process is executed using PC (Intel (R) Core (TM) i7–3770 CPU @ 3.40 GHz (8 CPUs), 16 GB, Windows 7–64 bits). Figure 4 shows that the attained cumulative PCR for 3 years and 49 sections using the ISA algorithm is 470, which is larger than that achieved by GA (PCR = 466). 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.

**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.

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. 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.


**Table 4.** Optimal maintenance activity plan by ISA algorithm to improve the pavement condition.

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.

**Figure 6.** Improvement of PCR.

**Figure 7.** Annual maintenance cost during three years.



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 9.** Optimal distribution of maintenance activities.

**Figure 10.** Optimal distribution of maintenance activities for road classes.
