The difference between traditional scooters and electric scooters is the convenience of refueling and charging process. Designing a complete infrastructure system is a necessary step if efforts to promote e-scooters are to meet with success. This study discusses the optimal location problem of locating charging stations—which is generally considered a location-allocation problem. There are two types of charging stations: charge stations and battery-exchange stations. The only one model in determining the location of either type of station tends to decrease the traditional utility compared to compound model traditional as this method tends not to set stations where they would serve the greatest number of customers. In addition, population density and land cost should be taken into account in determining where stations are set. We, therefore, propose a method that accounts for differences in population density and land cost in order to solve a multi-objective problem with maximum utility at minimum cost. A mathematical model is developed in which constraints pertaining to capacity and distance are considered. To find an optimal parameter for Multi-Objective Particle Swarm Optimization (MOPSO), generational distance (GD), maximum spread, spacing, and diversity metrics are applied. Finally, we research an angle-based focus method and determine the extent to which stations would be used in order to determine the optimal proportions of charging stations and battery-exchange stations. Moreover, according to the analysis we found that the installed ratio model of BES/BCS (Battery-exchange stations/Battery charging stations) is 6:5 in the downtown area and 1:6 in the outskirts of high population density areas. Besides, the BES/BCS ratio model is 1:13 in the downtown and only BCSs are installed in the outskirts of the low population density area.