## 4 Experimental Evaluation
### Example Background  
The system layout of the smart community is shown in Figure 5. We supposed that there are two service stations, located at (104, 32), (16, 69). Service station 1 has two robots, 1 and 2, and service station 2 has two robots, 3 and 4. The loadable capacity of these robots is 3, and their maximum distance is 300. Table 1 describes the 10 task requests in the delivery service area, and in this table, the serial number of the first column represents service customers. The second and third columns represent the X and Y coordinates of the service customers. The fourth column and the fifth column, respectively, represent the service time window required by the customer; the sixth column represents the time required for service at the customer point. For example, task 1 is located at coordinates (31, 82); it should start between time 0 and 2, and the execution of this task requires 0.5 s of service time. The charging time of the service station is supplemented according to the power loss of the robot during transportation. Since the simplified model considers that each robot is only transported once, it will return to the originating station to recharge or load the product after completing the task. As always, the robot has strict restrictions on the products that can be loaded. However, it is possible that a certain task is too heavy, so we divided this task into two tasks sharing the same location and time constraint, such as task A in the table. In our follow-up algorithm application, the distance between the two tasks is calculated according to the position of each task on the map. The specific calculation is shown in the following formula:  
\[\text{d}_{12}=\sqrt{(X_{1}-X_{2})^{2}+(Y_{1}-Y_{2})^{2}} \tag{39}\]  
Using the proposed algorithm, we obtained the best solution where the objective function value is 5496.2. As shown in Figure 6, it is the final assignment route of the 10 tasks. The optimal value iteration curve obtained by the algorithm is shown in Figure 7, and the specific task plan is shown in Table 2. Robot 1 leaves station 1 and returns to station 1 after performing tasks 2, 8, and 5. Robot 2 leaves station 1, performs tasks 10, 4, and 9, and then returns to station 1. Robot 3 leaves stations 2 and returns to station 2 after performing task 3, task 7, task 6, and task 1. It can be seen robot 4 is not used. Task A is finished by the robot 1 and 3 together.  
Figure 5: System layout of smart community delivery service using SR.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Task**} & \multicolumn{2}{c}{**Delivery Point**} & \multicolumn{2}{c}{**Earliest Service**} & \multicolumn{2}{c}{**Latest Service**} & \multicolumn{2}{c}{**Service Time**} \\ \cline{2-5}  & **X** & **Y** & **Time (\(F_{g}\))** & **Time (\(L_{g}\))** & **Time (\(L_{g}\))** & **(\(P_{g}\))** \\ \hline
1 & 31 & 82 & 0 & 2 & 0.4 \\
3 & 57 & 28 & 5 & 6 & 2 \\
4 & 90 & 94 & 1 & 3 & 0.5 \\
5 & 87 & 34 & 7 & 8 & 0.3 \\
6 & 24 & 16 & 2 & 6 & 0.2 \\
7 & 48 & 8 & 2 & 3 & 0.4 \\
8 & 71 & 32 & 7 & 9 & 0.6 \\
9 & 73 & 10 & 1 & 3 & 0.2 \\
10 & 104 & 56 & 6 & 7 & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Task delivery information of the robot.  
Figure 6: Final roadmap for 10 missions.  
Figure 7: Schematic illustrations of the search process.