## 4 Case Study Development and Results  
To illustrate the algorithm application and demonstrate the contribution of the proposed model to the electric vehicle charging station (EVCS) deployment, a case study consisting of a 200-EV fleet is considered. The area of interest in which the EVCS network is deployed is a square one, extending from \(-50\) to \(50\) in a coordinate system in which 1 length-unit may indicatively represent 100 m to simulate a medium-sized city of 100 km\({}^{2}\). The charging demand has been pseudo-randomly distributed all over the area of interest, while some specific sites concentrate a higher charging demand, representing places of different levels of interest. This type of allocation develops a balance between the necessary scattered distribution and some variation in demand concentration from point to point. In particular, there are 100 demand spots where 1, 2, or 3 EVs have been randomly allocated (Table S1). The number of charging stations varies from 1 to 25 in the core analysis, while larger numbers of stations are examined as part of a case study. The initial station allocation for the optimization deployment can be anyone, starting from the case of all stations coinciding at the center coordinates (this alternative is mostly used), progressing to a symmetrically scattered positioning within the application space, up to fully random placing in the area (Figure 2). The efficiency of the proposed model has been tested through a number of case studies that are summarized in Table 1 and described in the following subsections. The aim of the analysis is to provide insight and evidence of the algorithm capability in terms of both the mathematical solution vigor and its response potency to practical considerations. In each case, multiple runs have been made (usually three) to account for the result variability due to the probabilistic nature of the genetic algorithm. Different values of the GA parameters (initial population size, crossover, mutation rates, finishing criterion) have been analyzed and appropriately set. Figure 2: Demand scatter diagram (blue color) and charging station deployment (orange color) for the initial solution of the optimization: **(a)** center coordinates; **(b)** random distribution. Case Study 1: Station Allocation for EV Traveling Distance (Cost) Minimization at Different Numbers of Stations  
Initially, an exhaustive investigation of all scenarios representing the number of charging stations, from 1 to 25, was performed to develop the best station allocations (i.e., the lowest cumulative traveling distance of all EVs) at every number of stations. There are alternative configurations of station allocation that lead to approximately the same travel cost. Figure 3 presents three of them being developed by an initial station placement at the center of the area, a symmetrical initial station positioning, and a fully random initial station distribution within the analysis area. It appears that the algorithm converges to virtually the same station settlement regardless of the initial station distribution. Obviously, as the number of stations increases and the network becomes denser, the EV user can find a nearby station to charge and therefore reduce the travel distance. Figure 4 presents the average travel distance per EV, depending on the number of stations. The distance ranges from 4.4 to 20.6 for 25 and 3 stations, respectively (these numbers increase radically for 1 or 2 stations, not shown in the diagram). Figure 5 depicts 2 indicative networks deployed through Case Study 1 applications, which consist of 12 and 20 stations, respectively. To provide a rough indication of the required computational time,