High-altitude platform stations (HAPSs) are expected to provide ultrawide-coverage areas and disaster-resilient networks from the stratosphere at around 20 km by installing wireless equipment on HAPS. Because their altitude is much lower than that of communications satellites, HAPSs can provide mobile communications services directly to smartphones, which are commonly used in terrestrial networks, such as fourth generation Long Term Evolution. Considering the widespread nature of mobile broadband communications and the importance as a backup line in case of disaster, HAPSs are expected to provide a large capacity in the future. A cellular system with single-cell frequency reuse using multiple cells similar to terrestrial mobile communications should be introduced to achieve such a capacity. The number of cells that a HAPS can accommodate ranges from 1 to more than 100, depending on unmanned aerial vehicle (UAV) ability. By contrast, the optimal cell configuration, which depends on the number of available cells, has not been clarified in previous research. In this paper, we propose an optimization method for the cell configuration for HAPS mobile communications using a genetic algorithm, which can be generally applied regardless of the number of cells and can clarify the optimal cell configuration. Although many cells are required to achieve gigabit-class HAPS mobile communications, the heightened power consumption due to the large number of cells is a critical problem for UAVs. Thus, we also investigate the reduction of the total transmission power and demonstrate the feasibility of energy-efficient gigabit HAPS mobile communications with wide coverage.