## 4 Computational Experiments and Analyses
### Algorithm Comparison Experiment in VRPRSTW Model  
In order to verify the effectiveness of the proposed algorithm in the broken line soft time window model, the R101 data set was used in this experiment. One distribution center and the first 25 customers were selected from the data set for validation. The  
Figure 6: Variable neighborhood descent operator. (**a**) An example of gene fragment inversion process; (**b**) an example of single locus insertion process; (**c**) an example of double locus insertion process.  
maximum number of vehicles is 25, and the vehicle load capacity is 200 units. As there is minimal literature on vehicle routing problems with broken line soft time window under time-varying road network conditions, there are no studies that can be directly compared; this experiment refers to the broken line soft time windows model of [PERSON] et al. [35] to verify and analyze the algorithm. Aiming to minimize the total cost of transportation and distribution, [PERSON] et al. [35] constructed a general mathematical model for VRP with flexible time windows. Meanwhile, a commonality hyper-heuristic genetic algorithm was presented. The algorithm uses genetic algorithm as the upper search algorithm and three heuristic algorithms as the underlying search rules, and optimizes the algorithm by pre-sorting, local search, and global optimization. The difference between this model and this paper is that the vehicle speed is fixed, and the objective function only includes the \(C_{1}\) part of the objective function in this paper. Therefore, to make a comparison, the distance and time between different nodes are set in this experiment to be converted into the same unit, which is consistent with the literature and has the same objective function. The other parameters remain the same.  
The comparison between the optimal solution obtained by the algorithm and the reference literature is shown in Table 1, where TC represents the total cost (unit: yuan), IT represents number of iterations, VN represents the number of vehicles, VR represents vehicle route, LR represents vehicle loading rate, and RT represents return time.  
As shown in Table 1, the optimal solution of the objective function obtained by the variable neighborhood adaptive genetic algorithm in this paper was 4627.1, which was 2.95% lower than the reference. The number of iterations to reach the optimal solution was 14 generations, which was greatly reduced by 63.2%. The number of vehicles was four, which was the same as the reference. The return time of each vehicle was within the time window of the distribution center and did not violate the constraints of the time window. The optimal vehicle roadmap is shown in Figure 7. It can be seen that the variable neighborhood adaptive genetic algorithm proposed in this paper can better solve the vehicle path model with soft time windows, and the convergence speed is faster. The variable neighborhood adaptive genetic algorithm proposed in this paper was better than the hyper-heuristic genetic algorithm.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Variable Neighborhood Adaptive Genetic Algorithm**} & \multicolumn{6}{c}{**Hyper-Heuristic Genetic Algorithm**} \\ \hline
**TC** & **IT** & **VN** & **VR** & **LR/\%** & **RT** & **TC** & **IT** & **VN** & **VR** & **LR/\%** & **RT** \\ \hline \multirow{4}{*}{4627.1} & \multirow{4}{*}{14} & & 0-11-19-7-10-20-9-1-0 & 42.5 & 229.41 & & & & 0-5-16-18-8-17-13-0 & 47.0 & 220.25 \\  & & & 0-14-15-2-22-23-25-4-0 & 53.5 & 223.0 & & & 0-14-15-2-22-23-4-25-0 & 53.5 & 212.74 \\  & & & 0-21-12-3-24-0 & 23.0 & 190.0 & & & & 0-21-12-3-24-1-0 & 28.0 & 221.02 \\  & & & 0-5-16-6-18-8-17-13-0 & 47.0 & 221.26 & & & & & 0-11-19-7-10-20-9-0 & 37.5 & 218.40 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of experimental results in VRPSTW model.