## 2 Related Works  
### Studies on Capacitated Electric Vehicle Routing Problem with Time Windows  
The Capacitated Electric Vehicle Routing Problem with Time Windows (CEVRPTW) is an optimization problem involving routes where an electric vehicle starts from a depot, serves customers, and then completes its route at the depot. EVs have limited load capacity, and each customer has a time window, namely \"earliest start of service\" and \"latest start of service\". Within the time windows, each customer should be visited on the routes, and the load and charge status of the vehicles must be taken into account. In order to better analyze the studies on the EVRPTW, articles were searched for by searching the Web of Science with the keywords \"Electric Vehicle Routing Problem\" and \"Time Windows\". The graph of the obtained articles by year is given in Figure 1.  
The intense interest in this subject, especially in the last three years, can be seen in the figure. Researchers have provided comprehensive literature reviews on the subject. Among them, [PERSON] and [PERSON] (2019) analyzed EVRP variants, solution methods used in the literature, and the aspects that distinguish the studies from each other [9]. [PERSON] et al. (2022) included modeling approaches and different solution methods, such as machine learning, in their research results [10]. [PERSON] and [PERSON] (2023) analyzed the historical development of the problem and solution methods in detail and showed them statistically with graphs [11]. When the literature is examined, it can be seen that studies on EVRPTW obtained routes for minimizing the total distance in the first years. In the following years, it can be seen that the majority of studies were carried out on total time minimization and total energy minimization (Table 1). Figure 1: The number of papers on EVRPTW based on years (since 2007). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Study** & \begin{tabular}{c} **Minimize** \\ **Total** \\ **Distance** \\ \end{tabular} & \begin{tabular}{c} **Minimize** \\ **Total** \\ **Time** \\ \end{tabular} & \begin{tabular}{c} **Minimize** \\ **Total** \\ **Energy** \\ \end{tabular} & \
\begin{tabular}{c} **Minimize** \\ **Total** \\ **Recharging** \\ **Cost** \\ \end{tabular} &
\begin{tabular}{c} **Minimize** \\ **Total** \\ **Tardiness** \\ \end{tabular} \\ \hline [PERSON] and [PERSON], & & & & & \\
2011 [12] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2014 [13] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2014 [14] & & & & & \\ \hline [PERSON] and [PERSON], & & & & & \\
2015 [15] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2016 [16] & & & & & \\ \hline [PERSON] and [PERSON], & & & & & \\
2016 [17] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2017 [18] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2017 [19] & & & & & \\ \hline [PERSON] and [PERSON], & & & & & \\
2018 [20] & & & & & \\ \hline [PERSON] and [PERSON], & & & & & \\
2018 [21] & & & & & \\ \hline [PERSON] and [PERSON], & & & & & \\
2020 [22] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2020 [23] & & & & & \\ \hline [PERSON] and [PERSON], & & & & & \\
2021 [24] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2021 [25] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2022 [26] & & & & & \\ \hline [PERSON] and [PERSON], & & & & & \\
2022 [27] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2022 [28] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2022 [29] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2023 [30] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2023 [31] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2023 [32] & & & & & \\ \hline [PERSON] et al., & & & & & \\
2025 [33] & & & & & \\ \hline This Study & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Objective functions in papers on EVRP with time windows and charging station. The CEVRPTW is referred to as an NP-hard combinatorial optimization problem.