## 5 Description of Experiment and Analysis of Experimental Result
### Analysis of Experimental Result  
MATLAB programming was used to implement the above algorithm, and the test example was solved for 30 iterations. The calculation time was within 30 s, and the calculation efficiency was high. The calculation results were relatively stable: in the solution of the 30 times, all choose transit point 1, 2, and 3 for transit, the total number of paths is 9, the average value of the objective function is 8045.5, and the values of the objective function of the worst solution and the optimal solution are 8193 and 7969, respectively (the deviations from the mean are only 1.8% and 0.9%). The optimal solutions correspond to the primary path 2: namely DC-P1-P2-DC, DC-P3-DC. There are seven secondary paths, namely P1-8-7-6-2-P1, P1-5-1-3-4-P1, P2-28-27-26-29-30-P2, P3-24-21-23-25-P3, P3-22-20-19-18-P3, P3-11-14-12-10-P3, and P3-9-15-16-17-13-P3. The optimal solutions meet the requirements of the hard time window. Figures 4 and 5 show the convergence of the optimal solution and the optimal results of the example.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \(x\)**Coordinate/km** & \(y\)**Coordinate/km** & **Capacity/k** & & \(x\)**Coordinate/km** & \(y\)**Coordinate/km** & **Capacity/k** \\ \hline DC & 100 & 105 & 100 & P1 & 19 & 80 & 15 \\ \hline P2 & 74 & 57 & 20 & P3 & 23 & 25 & 25 \\ \hline P4 & 50 & 60 & 15 & P5 & 55 & 45 & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distribution center and transfer stations data.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \(x\)**Coordinate/km** & \(y\)**Coordinate/km** & **Capacity/k** & & \(x\)**Coordinate/km** & \(y\)**Coordinate/km** & **Capacity/k** \\ \hline DC & 100 & 105 & 100 & P1 & 19 & 80 & 15 \\ \hline P2 & 74 & 57 & 20 & P3 & 23 & 25 & 25 \\ \hline P4 & 50 & 60 & 15 & P5 & 55 & 45 & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distribution center and transfer stations data.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \(y\)**Coordinate/km** & \(y\)**Coordinate/km** & **Capacity/k** & & \(x\)**Coordinate/km** & \(y\)**Coordinate/km** & **Capacity/k** \\ \hline DC & 100 & 105 & 100 & P1 & 19 & 80 & 15 \\ \hline P2 & 74 & 57 & 20 & P3 & 23 & 25 & 25 \\ \hline P4 & 50 & 60 & 15 & P5 & 55 & 45 & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distribution center and transfer stations data.  
Different objective functions have no impact on the transfer cost, total number of paths, and cost of the first-level paths. The transit cost is 2212.5 yuan, the total number of routes is 9, and the cost value, delivery distance, and travel time in the first-stage routes the same. The second-stage cost and routes are different for different objective functions. The objective function with the shortest distance saves 17.95 km in distance and 26.92 min in time compared to that with the minimum total cost, incurring 131.25 yuan more in total cost. Therefore, cold-chain participants can choose different route schemes to maximise their interests. If the carrier is the main participant, the route scheme with the lowest total cost may be the best choice. If logistics outsourcing is involved, the shortest travel distance may be the best choice for logistics providers.