International audience; Air traffic management (ATM) represents a domain of emerging and challenging applications of mixed-integer nonlinear programming (MINLP). A number of problems arising in ATM lead naturally to optimization problems whose efficient and reliable solution constitutes a key ingredient of air traffic safety . The air traffic level currently attained in Europe is on the order of tens of thousands of flights per day, and it is expected to grow further on the world scale during the next 20 years. Increasing levels of traffic raise the problem of increasing the capacity of air sectors by better managing the air traffic. This requires increasing the level of automation in ATM, as pointed out in the context of the major projects Single European Sky ATM Research (SESAR)  in Europe and Next Generation Air Transportation System (NextGen)  in the United States, which are aimed at designing future ATM systems. Aircraft conflict detection and resolution in en route flights, and the related problem of conflict-free aircraft trajectory planning, are prominent examples of problems that urgently need to be addressed to ensure a higher level of automation in ATM, and consequently more efficiency and safety in air traffic. These problems still deserve investigation of both the identification of suitable mathematical models and the development of efficient and reliable solution methods and algorithms. Mixed-integer nonlinear optimization formulations appear particularly suitable, as they allow us to simultaneously consider continuous as well as discrete decision-making variables and model the complex nonlinear processes characterizing ATM systems.
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