Considering reducing the airspace congestion and the flight delay simultaneously, this paper formulates the airway network flow assignment (ANFA) problem as a multiobjective optimization model and presents a new multiobjective optimization framework to solve it. Firstly, an effective multi-island parallel evolution algorithm with multiple evolution populations is employed to improve the optimization capability. Secondly, the nondominated sorting genetic algorithm II is applied for each population. In addition, a cooperative coevolution algorithm is adapted to divide the ANFA problem into several low-dimensional biobjective optimization problems which are easier to deal with. Finally, in order to maintain the diversity of solutions and to avoid prematurity, a dynamic adjustment operator based on solution congestion degree is specifically designed for the ANFA problem. Simulation results using the real traffic data from China air route network and daily flight plans demonstrate that the proposed approach can improve the solution quality effectively, showing superiority to the existing approaches such as the multiobjective genetic algorithm, the well-known multiobjective evolutionary algorithm based on decomposition, and a cooperative coevolution multiobjective algorithm as well as other parallel evolution algorithms with different migration topology.