A co-evolution based method for optimizing crossing waypoints locations and adjacency relation in air route network

With a rapid development of air transportation, the optimization of Air Route Network (ARN) becomes critical to improve both airspace safety and efficiency in air traffic management system. This paper proposes a bi-objective ARN optimization model by considering its two coupled sub-problems, i.e., The optimization of Crossing Waypoints (CWs) locations and the optimization of Adjacency Relation (AR). A co-evolution based method, termed as CoM-ARN, is developed for solving the ARN optimization problem. In CoM-ARN, the locations of CWs and the AR are evolved in a cycle and co-evolved way. In the evolutionary process, Multi-Objective Comprehensive Learning Particle Swarm Optimizer (MOCLPSO) is adopted to globally search the CWs locations. Besides, an AR generator is specifically designed to generate edges of ARN using Delaunay Triangulation (DT) based on the locations of CWs. In addition, in order to minimize the flight cost, a refinement operator is proposed to fine-tune the locations of CWs guided by a virtual attractive force applied by the pairs of origin-destination airports on the CWs in an ARN. Empirical studies using real data of China airspace demonstrate that our method shows great superiority compared with other methods using Multi-Objective Evolutionary Algorithms (MOEAs) on the ARN optimization problem.