A Clustering-Based Algorithm for Aircraft Conflict Avoidance

Aircraft conflict avoidance is a critical issue in Air Traffic Management, which can be addressed, among others, by means of Mixed Integer Non-Linear Programming (MINLP) techniques. In this work we introduce a new approach to address, via velocity regulation, the problem of avoiding conflict for a set of aircraft flying in an air sector at cruise flight. Speed variations for all aircraft are to be minimized so that, at any time instant, the horizontal distance between each pair of aircraft is above a threshold security value. The problem can be expressed as a MINLP, solvable with standard MINLP solvers for a small number of aircraft, but intractable for instances of more realistic size. This motivates us the design of a cluster-based procedure. In our approach, aircraft are clustered into groups, so that within each cluster the aircraft are conflicting, while conflicts do not exist (or they are at least less severe) between aircraft in different clusters. Then a MINLP solver is used sequentially on each cluster to minimally modify the aircraft speeds so that conflicts within the cluster are solved, not creating new conflicts with aircraft in other clusters. Theoretical convergence of the procedure and preliminary numerical results will be discussed in the talk.