The design of a hybrid electric powertrain requires a complex optimization procedure because its performance will strongly depend on both the size of the components and the energy management strategy. The problem is particular critical in the aircraft field because of the strong constraints to be fulfilled (in particular in terms of weight and volume). The problem was addressed in the present investigation by linking an in-house simulation code for hybrid electric aircraft with a commercial many-objective optimization software. The design variables include the size of engine and electric motor, the specification of the battery (typology, nominal capacity, bus voltage), the cooling method of the motor and the battery management strategy. Several key performance indexes were suggested by the industrial partner. The four most important indexes were used as fitness functions: electric endurance, fuel consumption, take-off distance and powertrain volume. A design able to fulfill all the targets set by the industrial partner was found using an elimination-by-aspect approach applied to the overall Pareto front. The results of the algorithm were post-processed and some metrics were used to evaluate the performance of the genetic algorithm in solving the proposed optimization problem.