## 5 Result and Discussion
### Optimization Results and Analysis  
The distribution center and cabin in the validation area were relocated, and experiments were carried out in various application environments. Three cases were chosen for comparison. Multiple experiments were conducted on two algorithms to determine the superior performing data in each case. Each data table represents a set of Pareto solutions. A set of data was selected for display in Tables 3 and 4, with the remaining data in the Supplementary Materials. The NSGAII algorithm calculates the distribution distance based on the location coordinates, resulting in the straight-line distance between two location points. When obstacles are present between two points, the actual distribution route deviates from a straight line, leading to a longer distribution distance compared to the straight-line distance. Therefore, when comparing solutions, it is necessary to first modify the solutions obtained by the NSGAII algorithm. As shown in Table 5, D1 represents the delivery distance of the initial solution, and D2 is the modified distance after considering the impact of obstacles. In contrast, the HO-NSGAII algorithm accounts for obstacle distances, eliminating the need for distance modification (D3 = D4). The specific comparison results are presented in Table 5 and Figure 7, demonstrating superior calculation outcomes for the HO-NSGAII algorithm. In Table 5, m represents the number of vehicles, D1 and D3 represent the delivery distance \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Distribution Center** & **Distribution Route** & **Number of Vehicles** & **Distance (m)** \\ \hline \multirow{4}{*}{Test-01A} & DC1 & 5-1; 9-4 & \multirow{4}{*}{10} & \multirow{4}{*}{282.322} \\  & DC2 & 8-10-14; 7-3-2-6 & & \\ \multirow{4}{*}{Test-01B} & DC3 & 15-18; 12; 17-13-11 & & \\ \multirow{4}{*}{Test-01A} & DC4 & 22-24; 21 & \multirow{4}{*}{11} & \multirow{4}{*}{259.177} \\  & DC5 & 19-20-16; 23-25 & & \\ \hline \multirow{4}{*}{Test-01C} & DC1 & 9; 5-1; 4 & \multirow{4}{*}{12} & \multirow{4}{*}{257.177} \\  & DC2 & 8-10-14; 7-3-2-6 & & \\ \multirow{4}{*}{Test-01C} & DC3 & 15-18; 12; 17-13-11 & & \\ \cline{1-1}  & DC4 & 22-24; 21 & \multirow{4}{*}{19} & \multirow{4}{*}{257.177} \\  & DC5 & 19-20-16; 23-25 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: HO-NSGAII TEST-01 DATA. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Distribution Center** & **Distribution Route** & **Number of Vehicles** & **Distance (m)** \\ \hline \multirow{4}{*}{Test-01A} & DC1 & 8-5; 10-12-16; 9-4 & \multirow{4}{*}{10} & \multirow{4}{*}{297.166} \\  & DC2 & 7-11-13; 6-3-2-1 & & \\ \multirow{4}{*}{Test-01A} & DC4 & 22-24-25; 20-19 & & \\ \multirow{4}{*}{Test-01B} & DC5 & 23-17; 21-18; 15-14 & & \\ \hline \multirow{4}{*}{Test-01B} & DC1 & 8-5; 10-12-16; 9-4 & \multirow{4}{*}{11} & \multirow{4}{*}{268.431} \\  & DC2 & 7-11-13; 6-3-2-1 & & \\ \cline{1-1}  & DC4 & 17; 22-24; 20-19 & & \\ \cline{1-1}  & DC5 & 23-25; 21-18; 15-14 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: NSGAII TEST-01 DATA. before correction, while D2 and D4 represent the distance after correction. The distance gap is calculated as D2-D4, and the optimization rate is expressed as the distance gap divided by D2. Through the comparison of experimental data, it was observed that the Pareto solution set derived from the application of the HO-NSGAII algorithm under identical conditions exhibits superior performance. Specifically, the solution set demonstrates a shorter distribution distance when the number of vehicles is consistent. This improvement can be attributed to the direct consideration of obstacle distance within the algorithm, resulting in outcomes that better reflect real-world scenarios and mitigate the impact of obstacles on the route. Taking one set of data as an example, the actual calculation results are as follows: Figure 8 shows the distribution routes for two types of decentralized solutions (the red dashed line in the figure represents the revised actual route).