## 3 Proposed Model  
Research findings show that EV adoption requires deploying charging infrastructure (in terms of number and location) in a manner that is financially feasible as an investment and also manages to satisfy demands and overcome EV users' range anxiety. To support this goal, a bi-objective model is introduced for deploying EV charging stations for minimizing the total charging station network cost and maximizing the service quality/user satisfaction by reducing travel distance. The problem of charging station allocation in space falls within the general class of the Quadratic Assignment Problem (QAP). There are two general methods for dealing with this problem, the facility-to-location and the facility-to-site approach. In the first case, a number of potential sites for facility placement are predefined and the optimization algorithm seeks among them the best placement of the required facilities (stations). In the latter case, the algorithm freely assigns the facility to the solution space aiming at developing the best outcome based on the objective parameters and function. In the present formulation, the facility-to-site approach is primarily employed as it is difficult and rather impractical to predefine a reasonable number of potential station locations, except perhaps a few spots with known high charging demand (e.g., city downtown, shopping malls, etc.) or to exclude certain spots from the solution space if station deployment is infeasible (e.g., area topology,grid restrictions) or experience very low EV demand around it. The main shortcoming (and risk) of the facility-to-location approach is that, by selecting certain points for station deployment, one can omit other points that can potentially lead to better outcomes. In contrast, the facility-to-site approach can search all possible solutions but generally at the expense of higher computation effort. For the purpose of comparison, the problem has also been formulated as a facility-to-location one, based on grid discretization size, and the merits and demerits of both approaches are explored in Case Study 8 below. In this model development, an area of interest (A) is considered to represent a city or a neighborhood. Within this area, a number of charging stations (either predefined or open to the optimization process) are to be spatially allocated. In its general form, the model seeks two outcomes, the optimal number of stations and their spatial location to best serve the existing EV demand. Two cost (fitness) functions are considered, one for station deployment (f1) and the other for EV users traveling from each origin to its nearest station (f2), which is proportional to the traveling distance. As the decision for station placement is a one-time decision in advance of the operational phase, Euclidean distances have been considered in this formulation. The actual distances as well as the traffic conditions are rather dynamic and may be more effectively considered at the later stage of EV distribution to stations analysis. The mathematical form of the module is as follows. The demand points are set at predetermined coordinates (DPx, DPy). The decision parameters are the coordinates (CSx, CSy) of the charging stations. Two cost functions f1 and f2 are calculated as indicated in Equations (1) and (2). \[\mathrm{f1}=\mathrm{C_{station}}\cdot\mathrm{Si}=\left(\mathrm{C1}+\mathrm{C2 }+\mathrm{C3}\right)\cdot\mathrm{Si} \tag{1}\]  
where \(\mathrm{C_{station}}\) is the total cost for station deployment, comprising the construction (C1), operational (C2), and maintenance (C3) costs, and \(\mathrm{Si}\) is the number of stations. Although the above parameters have been taken here with fixed values in most of the analyses, it is easy to extend the problem structure to differentiate the costs depending on the size and deployment area of each station, as, for instance, in Case Study 4.