## 4 Case Study Development and Results
Although no full convergence on this goal is obtained, the solution indicates that most stations coincide with demand spots, while a few others attract EVs from more than one demand point, making the use of some other stations unnecessary. In Figure 12, the station allocations for the cases of 50 or 100 uniform demand points (with a total demand of 200 EVs) are presented to indicate the outcome. In the case of 50 stations, 4 of them are redundant (they do not attract any demand) and can be omitted. In the case of 100 stations, 23 of them are redundant. Case Study 8: Station Allocation for EV Travel Distance (Cost) Minimization at Grid Discretization Levels  
The issue of grid discretization is important for the following reasons. The area size under analysis may vary considerably along city sizes and the achievement of a certain level of detail is a desirable aspect. On the other hand, fine discretization may lead to difficulties in achieving an optimal solution in terms of both, the fitness value and the computational time. In this regard, a number of grid discretization alternatives have  
Figure 11: Indicative charging station deployment optimization results for Case Study 7: (**a**) 50-station charging network; (**b**) 100-station charging network (demand points in blue color, charging stations in orange color). Figure 12: Indicative charging station deployment optimization results for Case Study 7: (**a**) 50 demand points; (**b**) 100 demand points (demand points in blue color, charging stations in orange color). been examined as part of this investigation. All the solutions presented above have been obtained by considering station coordinates with integer values. In the present analysis, different discretization levels are considered in the basic scenario. As the discretization level becomes coarser, the problem progressively moves from a facility-to-site to a facility-to-location formulation. For instance, if the grid unit is 10, there are 11 by 11 possible locations for allocating the charging stations in the \(-\)50 to 50 range of the rectangle area, and the objective is to select which of these points will host a station. Such rough discretization may be preferable if the application space is widespread, e.g., in large cities. As the number of possible locations decreases, the number of alternative solutions also decreases, as does the optimization quality in terms of the fitness value. On the other hand, a possible benefit of such rough discretization may be any reduction in computation time. Not surprisingly, the computational time is not improved because the required computations are virtually the same, as the only change is the set of values that the decision parameters (station coordinates) can choose from. In fact, even with a fine decimal level of discretization, the computation burden is not increased, and the resulting fitness value is comparable to that of the integer discretization. Figure 13 illustrates the results for 10 stations and discretization levels of 1 and 10 units. The total traveling distance for discretization levels of 1, 2, 5, and 10 units is 2042, 2045, 2078, and 2193, respectively. The lowest of the above values is also achieved with any decimal discretization of the application area. Case Study 9: Station Allocation for EV Travel Distance (Cost) Minimization at Progressive Station Network Deployment  
This analysis refers to the practical consideration of the dynamic demand evolvement over time. The EV market and charging demand are still in their infancy in many places around the world but they grow fast. Although a full-scale station development could be done now with the expectation of full market growth in a few years, an alternative cost-effective solution is the ongoing (phased) station development. This approach balances the demand growth and the service provision without binding unnecessary resources for building several stations from the beginning to serve initially sparse EV charging demand.