## 3 Materials and Methods
### Proposed Adaptive Large Neighborhood Search
#### 3.2.1 Initial Solution
It inserts the charging station with the lowest cost that will make the route feasible. This operator adds not only the cost of traveling from one point to the station but also the cost of traveling from the station to the next point. #### 3.2.5 Local Search

Local search (LS) methods were included in this study due to their fast applicability and ability to produce effective solutions, and their aim was to search the solution space faster. In order to apply LS methods, the VNS-based procedure was used [13; 50; 51]. The pseudocode is given in Algorithm 11. ```
Input:\(S^{current}\), \(k_{max}\) \(k\gets 1\) while\(k\leq k_{max}\)do  Select \(LS\) operator \(\Omega^{LS}\) using Roulette Wheel Selection \(S^{new}\)\(\leftarrow\)Local_Search(\(S^{current}\)) if\(f(S^{new})\)\(<\)\(f(S^{current})\)then \(S^{current}\gets S^{new}\) \(k\gets 1\) else \(k\gets k+1\) endif endwhile return\(S^{current}\)
```

**Algorithm 11** VNS-based LS

Two groups of LS methods are used for the problem: intra-route (Intra) and inter-route (Inter) [9; 27]. In **IntraRelocate**, a customer selected from a route is moved to another location on the same route. This process aims to reduce the cost of a single route. In **IntraExchange**, the locations of two customers selected on a route are swapped. In **IntraOrOpt**, a consecutive customer segment selected on a route is moved to another location. It can be considered the relocation of a customer group within a route. In **IntraTwoOpt**, two customer arcs selected on a route are arranged in reverse on the route. **InterRelocate** is the process of moving a customer selected on a route to a different route. **InterExchange** is the process of swapping customers selected from two different routes with each other. **InterCrossExchange** is the mutual relocation of customer segments selected from two different routes. **Inter2 Opt* is the process of swapping customer segments selected on two different routes crosswise on the routes. ## 4 Experimental Results

### Validation of the Adaptive Large Neighborhood Search

The CEVRPTW dataset containing the Eskisehir Osmangazi University campus environment data is used in this study [52; 53]. For instance, the RC05 test problem with five customers is given in Table 3.

The map of the ESOGU environment, which represents customers, charging stations, and warehouses in the datasets, is given in Figure 3.

Test problems were solved in Python 3.12 on a Windows 10 PC with an AMD Ryzen 7 4700 U @2.00 GHz processor and 8 GB RAM. The vehicle parameters were an energy consumption rate of 1.0, a charging rate of 0.18, a battery capacity of 3000 kWs, a speed of 12.5 m/s, and a load capacity of 350 kg. For large-size problems, the algorithm parameters were chosen as an iteration number of 8000, a cooling rate of 0.9980, an initial temperature of 10,000, a number of iterations without improvement (\(N\)) of 8, a number of route removal frequency (\(K\)) of 25, and a weight update frequency (\(Z\)) of 10. For small problems (5-10-20), the solution was obtained with 1000 iterations while keeping the other parameters the same. Each test problem was solved 10 times by ALNS, and the best results obtained were tabulated. In addition, optimal results were obtained using CPLEX Solver for the objective function of minimizing the total distance by using a full charging strategy. Exact solutions with zero tardiness are compared with solutions obtained by ALNS in Table 4. In large-scale problems with 60 customers, the mathematical model could not provide solutions in a reasonable time. The results were obtained by CPLEX in a three-hour time limit. Figure 3: ESOGU campus environment. Created using OpenStreetMap and Folium. Map data © Esri, Maxar, Earthstar Geographics, and the GIS User Community.