Air traffic management is a complex system. Currently in transition, one of the main evolutions to this system is the search for an automatic method for solving air-traffic conflict problems. In this thesis, we present a new way to tackle the problem. First, we introduce a new smooth trajectory model based on B-splines thus allowing us to define a trajectory using only a few parameters. Using this trajectory model, we define a new formulation for the conflict resolution problem yielding a continuous optimization problem. It relies on a semi-infinite programming formulation of the separation constraints between two aircraft. Our formulation enables the calculation of the functions involved in the optimization problem. We use three different optimization methods to solve our problem. A stochastic global optimization method has first been tested : a genetic algorithm, of the type commonly used in air-traffic conflict resolution. Two local optimization methods are also implemented : an interior point method and a derivative-free optimization method. Finally, we present promising numerical results showing the viability of local optimization method for the air-traffic conflict resolution problem. More precisely, our methodology, relying on a parsimonious smooth trajectory model and local optimization methods applied to our mathematical formulation of the problem, is a credible alternative for the air-traffic conflict resolution problem.
Modélisation mathématique et résolution automatique de conflits par algorithmes génétiques et par optimisation locale continue