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For short take-off and landing (STOL) aircraft, a parallel hybrid-electric propulsion system potentially offers superior performance compared to a conventional propulsion system, because the short-take-off power requirement is much higher than the cruise power requirement. This power-matching problem can be solved with a balanced hybrid propulsion system. However, there is a trade-off between wing loading, power loading, the level of hybridization, as well as range and take-off distance. An optimization method can vary design variables in such a way that a minimum of a particular objective is attained. In this paper, a comparison between the optimization results for minimum mass, minimum consumed primary energy, and minimum cost is conducted. A new initial sizing algorithm for general aviation aircraft with hybrid-electric propulsion systems is applied. This initial sizing methodology covers point performance, mission performance analysis, the weight estimation process, and cost estimation. The methodology is applied to the design of a STOL general aviation aircraft, intended for on-demand air mobility operations. The aircraft is sized to carry eight passengers over a distance of 500 km, while able to take off and land from short airstrips. Results indicate that parallel hybrid-electric propulsion systems must be considered for future STOL aircraft.