## 4 Results and Discussion  
The parameters used to create the paths can be found in Table 2. In the table, there are two parameters that rely on parallel computing processes, which include the number of ants in the lower-level path generation and the number of CPUs used in the higher-level path generation. In the lower-level path generation, a single ant was simulated by each CPU in parallel. By doing so, the computation time for each iteration is significantly reduced. In the higher-level path generation, the CPUs were used to compute chunks of the population in parallel. Specifically, five CPUs were used to compute four solutions each (for a population size of 20) in parallel. When more CPUs are used, more time is required for resource allocation. When fewer CPUs are used, each CPU computes too many solutions. Therefore, the number of CPUs was optimized to yield the least computation time such that the resource allocation time and population distribution were effectively balanced. Additionally, the ACO parameters were selected based on various simulated experiments to yield satisfying results within a manageable timeframe. As for the GA, these parameters were selected based on a general rule-of-thumb (high crossover and low mutation) combined with previous project experience with route optimization and scheduling [28; 33]. To evaluate the effectiveness of the proposed methods, several different test scenarios were proposed. A summary of the test scenarios can be found in Table 3, and the respective vehicle starting locations can be seen in Figure 14. As highlighted in Table 3, two breakdown scenarios were used to observe the feasibility of the real-time scheduling capabilities of the higher-level path generation. In these scenarios, the rest of the path left by the out-of-service vehicle should be covered by one (or several) of the remaining vehicles. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Value** \\ \hline \multirow{5}{*}{Lower-Level Path Generation (ACO)} & \(\alpha\) (Pheromone Influence) & 0.1 \\ \cline{2-3}  & \(\beta\) (Edge Distance Influence) & 0.3 \\ \cline{2-3}  & \(\rho\) (Pheromone Evaporation Rate) & 0.4 \\ \cline{2-3}  & Number of Ants * & 24 \\ \cline{2-3}  & Iterations & 250 \\ \hline \multirow{5}{*}{Higher-Level Path Generation (GA)} & Generations & 60 \\ \cline{2-3}  & Population Size & 20 \\ \cline{1-1} \cline{2-3}  & Crossover Probability & 0.9 \\ \cline{1-1} \cline{2-3}  & Mutation Probability & 0.05 \\ \cline{1-1} \cline{2-3}  & CPUs * & 5 \\ \hline \hline \end{tabular}  
* These parameters are used for parallel computing.  
\end{table} 
Table 2: Parameters used in the lower- and higher-level path generation algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **Number of** **Vehicles** & **Operating Conditions** & **Starting Locations** \\ \hline
1 & 3 & Normal & Different Starting Locations 1 [FOOTNOTE:1]Footnote 1: The starting locations are depicted in Figure 14a. 2 The starting location is depicted in Figure 14b. 3 The starting location is depicted in Figure 14c. 2 The starting location is depicted in Figure 14c. 2 The starting location is depicted in Figure 14c. 3 The starting location is depicted in Figure 14c. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test case scenarios for the proposed research. The total distance and overall travel time for all scenarios are summarized in Table 4. As seen in Table 4, the starting location for the vehicles has an influence on the total distance and overall operation time. This is evident in Scenarios 1 to 3 (the only difference in these scenarios is the starting location, but different statistics are seen). However, the vehicle starting/ending locations were not optimized in this study. The vehicle's starting/ending locations are simply places where the vehicles are stored and thus used as an input to the developed path generation methods. Also, an arbitrary ending point was selected for this study.