<p>This paper focuses on the trajectory optimization based Auxiliary Power Unit (APU) for an Extended Range Electric Vehicle (EREV). Firstly, a new three-zone control strategy has been proposed to optimize the APU steady-state operation, and the simulation result show significant enhancements in fuel efficiency compared to the traditional thermostat and power-following control strategy. Furthermore, low-frequency noise and vibrations generated by the APU during transient operations are the primary factors affecting passenger comfort, which are closely associated with transient operational trajectory of the APU. In order to address the fuel consumption and NVH (Noise, Vibration, and Harshness) challenges in EREV during dynamic operation, a multi-objective optimization model is developed. The multi-objective particle swarm algorithm and weighted scaling method are employed to solve the model, obtaining the transient operating trajectory of the APU. Finally, the method proposed is validated on a test bench and compared with single-objective optimization method based on the best BSFC (Brake Specific Fuel Consumption) and traditional optimization method. The results indicate that the multi-objective operational trajectory proposed can effectively improve the NVH performance of the APU at the cost of a slight increase(3.9%) in fuel consumption. Although a slight increase in fuel consumption occurs during the transient switching process, the overall energy efficiency of the APU system remains improved due to the high-efficiency steady-state operation enabled by the three-zone control strategy.</p>