In order to improve the output performance of permanent magnet assisted synchronous reluctance motor (PMa-SynRM), a multi-objective optimization design method for external rotor PMa-SynRM based on kernel extreme learning machine(KELM) and fast non-dominated sorting genetic algorithm (NSGA-II) was proposed. Firstly, the preliminary design of the PMa-SynRM rotor magnetic barrier was carried out and the working principle of the PMa-SynRM was analyzed. Secondly, the influence of each design variable on the optimization goal was evaluated through comprehensive sensitivity analysis, and the main optimization parameters were selected. Thirdly, with high output torque, high efficiency and low torque ripple as the optimization goals, a surrogate model based on KELM was established. Finally, NSGA-II was used for global optimization, and the optimal solution was selected from the Pareto frontier generated by NSGA-II, which was verified by finite element analysis. The simulation results show that the average torque of the optimized motor is increased by 15.83%, the torque ripple is reduced by 60.27%, and the efficiency of the optimized motor is also improved compared with the initial motor, which verifies the effectiveness of the optimized design method proposed in this paper.