With the development of More Electrical Aircraft (MEA), the electrification of secondary power systems in aircraft is becoming more and more common. As the key power conversion device, the dual active bridge (DAB) converter is the power interface for the energy storage system with the high voltage direct current (HVDC) bus in aircraft electrical power systems. In this paper, a DAB DC-DC converter is designed to meet aviation requirements. The extended dual phase shifted control strategy is adopted, and a multi-objective genetic algorithm is applied to optimize its operating performance. Considering the three indicators of inductance current root mean square root (RMS) value, negative reverse power and direct current (DC) bias component of the current for the high frequency transformer as the optimization objectives, the DAB converter's optimization model is derived to achieve soft switching as the main constraint condition. Optimized methods of controlling quantity for the DAB based on the evolution and genetic algorithm is used to solve the model, and a number of optimal control parameters are obtained under different load conditions. The results of digital, hard-in-loop simulation and hardware prototype experiments show that the three performance indexes are all suppressed greatly, and the optimization method proposed in this paper is reasonable. The work of this paper provides a theoretical basis and researching method for the multi-objective optimization of the power converter in the aircraft electrical power system.