# Vehicle Routing Problem with Drones Considering Time Windows and Dynamic Demand
## 5 Computational Experiments
### Algorithm Performance Test  
#### 5.1.1 Comparison of the Results of Different Algorithms  
The enumeration method (EM) is an algorithm for finding the optimal solution to a problem by enumerating all possible solutions. It has the characteristics of a simple principle and easy proof of correctness. Genetic algorithm (GA), simulated annealing (SA), and traditional CHOA are widely used to solve various optimization problems and are also suitable for solving drone-vehicle routing problems with time windows. To evaluate the effectiveness of the algorithm, this paper compares the results of SACHOA with those of EM, GA, SA, and CHOA. The results are presented in Table 3, including the name, scale, number of truck service customers (T_C) in the test data set, the optimal solution value of each algorithm, and the difference, \(GAP^{Y}\), between them. \(GAP^{Y}=(SACHOA-Y)/Y\times 100\%\), where \(Y\) represents EM/GA/SA/CHOA. Table 3 demonstrates that while EM can produce optimal solutions for VRPDTW problems on smaller scales, it falls short in solving examples with 20 customers within a reasonable timeframe. This is due to the significant increase in solution time as the number of customers increases, resulting from an expanded solution space. Alternatively, GA, SA, CHOA, and SACHOA are better suited for such problems, with SACHOA achieving superior results. In the case of small-scale test datasets, such as R101_10, each algorithm performs consistently and produces optimal solutions. This is attributed to the smaller search space and lower difficulty in these datasets, resulting in relatively similar algorithm performances. Nevertheless, for medium-scale datasets such as C102_25, there are slight differences in the results of the algorithms, although overall performance remains quite similar, demonstrating that the performance of the algorithms starts to show differences for moderate-scale datasets. In contrast, for large-scale datasets like RC101_100, the algorithms vary significantly in performance, with SACHOA outperforming the others. These findings indicate that SACHOA has greater adaptability and robustness when tackling larger-scale problems. In addition, the number and location of customer nodes served by trucks have a direct impact on the delivery costs. When the number of customers served by trucks is low, the delivery cost is small; when the number of customers served by trucks is high, the delivery cost is high, which is the result of the fact that the unit delivery cost of drones is lower than that of trucks. Consequently, the more customer nodes drones serve, the greater the reduction in delivery costs. From the perspective of the delivery location of the customer nodes from the truck service, when delivery to the customer nodes from the truck service is relatively centralized, the delivery cost is smaller. The reason for this is that location dispersion leads to a small change in the length of the truck route, which is not conducive to a reduction in the delivery cost; this is the actual delivery situation. Figure 7 depicts the convergence diagrams for SACHOA, CHOA, SA, and GA algorithms when solving example RC101_25. The results show that the SACHOA algorithm has the following advantages over other algorithms when dealing with the VRPDTW problem: first, the SACHOA algorithm is outstanding in the speed of convergence to the relatively  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Test Name** & \begin{tabular}{c} **Number** \\ \_Node** \\ \end{tabular}