To fully exploit the flexible use of airspace and its capacity within the arrival airspace, the multi-objective optimization problem of flight arrival paths was studied. Considering constraints such as safety intervals, a path assignment model was constructed with the objectives of minimizing traffic density and average arrival time of flights. A non-dominated sorting genetic algorithm-II(NSGA-II) was designed to solve the optimization problem. The optimization results show that a 12.23% reduction in traffic density and a 14.32% decrease in average arrival time after path assignment. The algorithm simultaneously categorizes a set of flights that required adjustment to their arrival paths. The optimized solution underwent total airspace and airport modeller(TAAM) simulation validation. The results demonstrate that path assignment resulted in a 10% increase in instantaneous aircraft movements within the airspace under high traffic conditions. The sector simulation load decreases by 9.3%, and the average five-sided landing time intervals are small and uniform, with a maximum reduction of 18.23%. The feasibility of path assignment was verified. The research results can effectively enhance the utilization rate of the arrival airspace, flight arrival efficiency, and runway arrival capacity. It assists in the traffic management of the arrival airspace or controller decision-making.