## 4 Case Study Development and Results
This progressive development may also be of benefit if the EV demand, besides increasing, presents a different space allocation in the future, as a result of city development. For the purposes of the present study, it is assumed that the EV demand retains the same space allocation which is also a realistic scenario. The analysis is performed in two stages. Initially, 10 charging stations are optimally allocated (with reference to the basic scenario). In the second phase, these 10 stations are considered fixed, and another 10 stations are further  
Figure 13: Indicative deployment optimization results of a 10-station network for different grid discretization: (**a**) 1 unit discretization; (**b**) 10 units discretization (demand points in blue color, charging stations in orange color). allocated in an optimal way to improve the total EV traveling distance. The final solution is compared to the one with a single-phase allocation of 20 charging stations. Figure 14 comparatively illustrates the two scenarios, one deploying 20 stations at once and a second deploying 10 stations nowadays and another 10 stations in a future stage. It can be seen that the total traveling distance in these two cases is 1170 and 1236, respectively, indicating an increase in the second case of about 6%. Case Study 10: Station Allocation for EV Travel Distance (Cost) Minimization Considering EV Range Capacity and Infeasible Zones for Station Deployment  
In this part of the analysis, two further cases are considered, the implication of EV range limitations to reach a station and the potential existence of infeasible zones for station deployment. In regard to the traveling range limitation, the 12-station network that was examined in Case Study 1 is revisited. Different range thresholds are considered to indicate the maximum distance the EVs can travel. Table 3 illustrates some indicative results. If the permittable range is higher than 27.31 units, which is the maximum EV traveling distance in the case of free station allocation, the optimization results coincide with those of Case Study 1 in terms of station spatial distribution and the objective function value. Below the threshold of 27.31 units, station reallocation is needed to satisfy the maximum range constraint at the expense, however, of the total (and average) traveling distance. The lowest limit of the maximum traveling distance that can lead to a feasible solution is 17.03 and can be found by minimizing the max trip distance of all EVs. The second part of this Case study examines the practical implication of having infeasible zones for station deployment within the search area. This case can be considered a special instance of Case Study 4 (different cost zones) by setting an extremely high-cost value within the infeasible zones. An indicative example is presented in Figure 15  
Figure 14: Indicative deployment optimization results of a 20-station network: (**a**) single-phase allocation; (**b**) two-phase allocation (demand points in blue color, charging stations in orange color). \begin{table}
\begin{tabular}{c c c c} \hline \hline
27.31 & 1762 & 8.81 & 27.31 \\
26 & 1769 & 8.85 & 25.50 \\
24 & 1779 & 8.90 & 23.71 \\
22 & 1797 & 8.98 & 21.93 \\
20 & 1871  
where the inner zone is considered to be infeasible for station deployment. The results indicate that five stations initially allocated in this zone (green color) are moved outside it with some of them placed just outside the infeasible region to serve EVs from this area. The corresponding fitness values for the two cases in terms of total distance are 948 and 1019, respectively.