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This paper tackles the collision-avoidance problem in air traffic management. The problem consists of deciding the best strategy for new aircraft configurations (velocity and altitude changes) such that all conflicts in the airspace, i.e., the loss of the minimum safety distance that has to be kept between two aircraft, are avoided. A mixed 0-1 linear optimization model based on geometric transformations for collision avoidance between an arbitrary number of aircraft in the airspace is developed. Knowing the initial coordinates, angle direction, and level flight, the new configuration for each aircraft is established by minimizing several objective functions, e.g., velocity variation and total number of changes (velocity and altitude), and forcing to return to the original flight configuration when no aircraft are in conflict. Due to the small computational time for the execution, the new configuration approach can be used in real time by using optimization software.