## 7 Conclusions  
In order to improve the defects of the AEFA, this paper proposed an improved artificial electric field algorithm (SC-AEFA) that integrates the sine cosine mechanism. First, the iterative formula of the original artificial electric field algorithm was improved to reduce the influence of the step size in the later iteration to highlight the importance of individual positions. In addition, a repulsive factor was introduced in the iterative process to keep away from the current worst individual. Second, some parameters of the sine cosine algorithm were improved, so that the sine cosine algorithm could better control the dynamic balance between the global search and local search. Finally, the improved sine cosine iterative formula was introduced into the artificial electric field algorithm, so that the algorithm can increase the scope of the global search and improve the ability of local optimization. Through the comparison experiment of the test functions, it was proven that the optimization accuracy of the algorithm proposed was significantly improved, and the stability had more significant advantages.  
In addition, this paper took the vehicle routing problem with time window constraints as the research object and established the VRPTW with the vehicle cost, distance cost, and time window penalty cost as the objective function. This problem was solved by the ACO algorithm, BOA, AEFA, and SC-AEFA. The results showed that the optimization ability of the SC-AEFA was significantly improved compared to the AEFA, and that it had a certain robustness. The results obtained by the algorithm proposed are not the best solution, so there is still much room for improvement in the performance of the algorithm. The main problem we face is that we cannot find the best solution range in the global search, so we cannot find the best result in the local search. In the following research, based on this problem, strategies to enhance the global search will be added into the algorithm.  
Future research can be further carried out from the following two aspects:  
Methods for solving discrete problems such as path optimization and location selection can be studied in more depth, since the artificial electric field algorithm is more suitable for solving discrete problems. The improvement mechanism of this paper is relatively simple. The performance of the artificial electric field algorithm has not been fully explored, so the algorithm still has much room for improvement. Applying the improved artificial electric  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **The Optimal Value** & **The Worst Value** & **The Average Value** & \multicolumn{2}{c}{**The Earliest**} \\  & & & & **Convergence Number** \\ \hline AEFA & 562.78 & 593.49 & 560.78 & 40 \\ SC-AEFA & 556.12 & 568.38 & 556.86 & 23 \\ BOA & 559.66 & 677.94 & 561.36 & 37 \\ ACO & 656.01 & 679.23 & 678.75 & 33 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The comparison of results.  
field algorithm to the system scheduling problem can be carried out to further verify the performance of the algorithm in future studies.  
Conceptualization, H.Z.; Methodology, H.Z. and J.X.; Writing--original draft preparation, H.Z.; Writing--review and editing, J.X.; Software, H.C. and G.Y.; Validation, L.Z., J.X., L.Z. and J.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Guangxi Science and Technology Base and Special Talents Project under Grant No. 2021 AC19436, the Key Laboratory of Software Engineering in Guangxi Minzu University under Grant No. 2022-18 XJSY-03, the Talent Introduction Project of Guangxi Minzu University under Grant No.2020 KJQD05, the Innovation Training Program for College Students under Grant No.202110608009, and the Research Foundation for Civil Aviation University of China (3122022 PT02).  
Not applicable.  
The data used to support the findings of this study are included within the article.  
The authors declare no conflict of interest.