Multiobjective 4D Optimization of a Trajectory-Based Air Traffic Management

Abstract

Weather conditions have a major impact on air traffic management in planning as well as in flight. Since the volcanic eruptions in 2010 caused enormous disturbance of the air traffic over Europe, much effort has gone into the task of finding clear routes in case of occurrence of aviation obstacles like ash clouds or hazardous weather. In this contribution the development of a 4D optimization model of a trajectory-based air traffic management is described. The model makes use of a multicriteria cost function which takes into account fuel flow, time, distance and the specialized performance parameters for an aircraft. We create an individual network for each flight in which the single flight routing problem can be formulated as a minimum cost single commodity network flow problem, wellknown as the shortest path problem. Solutions are generated using the A* algorithm, which is a modified version of Dijkstra's algorithm. The multiple flight routing problem is formulated as a dynamic multicommodity network flow problem. We generate feasible solutions using Lagrangian relaxation in combination with a Lagrangian based heuristic. The Lagrangian subproblem decomposes into several single commodity network flow problems in each iteration, and thus the solution approach makes use of the methods developed for the single flight routing problem.