Abstract

Recently, the long-term conflict avoidance approaches based on large-scale flights scheduling have attracted much attention due to their ability to provide solutions from a global point of view. However, the current approaches which focus only on a single objective with the aim of minimizing the total delay and the number of conflicts, cannot provide the controllers with variety of optional solutions, representing different trade-offs. Furthermore, the flight track error is often overlooked in the current research. Therefore, in order to make the model more realistic, in this paper, we formulate the long-term conflict avoidance problem as a multi-objective optimization problem which minimizes the total delay and reduces the number of conflicts simultaneously. As a complex air route networks needs to accommodate thousands of flights, the problem is a large-scale combinatorial optimization problem with tightly coupled variables, which make the problem difficult to deal with. Hence, in order to further improve the searching capability of the solution algorithm, a cooperative co-evolution (CC) algorithm is also introduced to divide the complex problem into several low dimensional sub-problems which are easier to solve. Moreover, a dynamic grouping strategy based on the conflict detection is proposed to improve the optimization efficiency and to avoid premature convergence. The well-known multi-objective evolutionary algorithm based on decomposition (MOEA/D) is then employed to tackle each sub-problem. Computational results using real traffic data from the Chinese air route network demonstrate that the proposed approach obtained better non-dominated solutions in a more effective manner than the existing approaches, including the multi-objective genetic algorithm (MOGA), NSGAII, and MOEA/D. The results also show that our approach provided satisfactory solutions for controllers from a practical point of view.