## 4 Computational Experiments and Analyses
### Algorithm Comparison Experiment in TDGVRPSTW Model  
In order to evaluate the efficiency of the proposed approach in the TDGVRPSTW model, two GA-based algorithms are used for comparison. There are many variants of GA for GVRP model [38], among which adaptive genetic algorithm (AGA) and hybrid genetic algorithm (HGA) are commonly used [39]. AGA and HGA are coded as follows:  
* The initial population of both algorithms is generated by random method. * The adaptive function, crossover operator, and mutation operator in AGA are consistent with those described in Section 3.4. * HGA is composed of GA and local search, which are called sequentially. * The exchange method of local search is to exchange the path fragments of any two individuals in the population [40]. Table 2 lists the results obtained by the three algorithms. Each data set contains data for one distribution center and 25 customers, with a maximum of 25 vehicles. The total cost (TC) in this experiment refers to the objective function of this model: Equation (5). VNAGA is the variable neighborhood adaptive genetic algorithm, which is the proposed approach in this paper. Gap_a% and Gap_h%, respectively, represent the optimized percentage of TC values of AGA and HGA, for example, \(Gap\_a\%=(AGA_{TC}-VNAGA_{TC})/VNAGA_{TC}\times 100\%\). As shown in Table 2, the average optimization percentage of TC value of the proposed approach compared with AGA and HGA is 2.09% and 1.42%, respectively. For the selected 12 data sets, the TC values of the proposed approach were superior to AGA and HGA, and \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Data set**} & \multicolumn{2}{c}{**VNAGA**} & \multicolumn{2}{c}{**AGA**} & \multicolumn{2}{c}{**HGA**} & \multirow{2}{*}{**Gap\_a\%**} & \multirow{2}{*}{**Gap\_h\%**} \\ \cline{2-2} \cline{6-8}  & **TC** & **IT** & **TC** & **IT** & **TC** & **IT** & **IT** \\ \hline C102 & 3534.94 & 34 & 3607.76 & 46 & 3586.20 & 41 & 2.06 & 1.45 \\ C104 & 3333.77 & 22 & 3397.78 & 35 & 3371.44 & 23 & 1.92 & 1.13 \\ C106 & 4291.84 & 18 & 4540.34 & 42 & 4427.89 & 16 & 5.79 & 3.17 \\ C204 & 4097.12 & 32 & 4180.29 & 59 & 4187.67 & 28 & 2.03 & 2.21 \\ R103 & 5520.32 & 65 & 5616.37 & 71 & 5620.00 & 89 & 1.74 & 1.86 \\ R109 & 5880.64 & 30 & 5968.69 & 52 & 5921.22 & 24 & 1.50 & 0.69 \\ R111 & 5423.99 & 51 & 5473.31 & 95 & 5473.84 & 53 & 0.91 & 0.92 \\ R204 & 4632.26 & 36 & 4648.47 & 34 & 4640.60 & 47 & 0.35 & 0.18 \\ RC103 & 4901.52 & 27 & 5091.85 & 45 & 5012.69 & 20 & 3.88 & 2.27 \\ RC104 & 4303.35 & 53 & 4370.36 & 64 & 4351.55 & 66 & 1.56 & 1.12 \\ RC107 & 4275.99 & 24 & 4360.23 & 58 & 4307.63 & 31 & 1.97 & 0.74 \\ RC208 & 4340.03 & 36 & 4400.36 & 47 & 4398.62 & 39 & 1.39 & 1.35 \\ Average & 4544.65 & 36 & 4637.98 & 54 & 4608.53 & 40 & 2.09 & 1.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of experimental results in TDGVRPSTW model. Figure 7: Optimal distribution roadmap in the comparison experiment. the proposed approach had a greater advantage over AGA than HGA. For C-type data sets and RC data sets, the proposed approach has a relatively large advantage over the two algorithms, while for R-type data sets, the proposed approach does not have a large advantage. This shows that the proposed approach can obtain good optimal solutions for centrally distributed customers and mixed customers, while the proposed scheme has no obvious advantages for uniformly distributed customers. The IT value of the proposed approach is better than that of the other two algorithms, and the advantages of the proposed approach compared with AGA are greater than those of HGA. For the selected 12 data sets, the IT values of the proposed approach are all better than the corresponding values of AGA, and most of the IT values of the proposed approach are better than the corresponding values of HGA. Moreover, according to the average results of TC and IT, the proposed method is superior to HGA, and HGA is superior to AGA.