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.

The aircraft conflict detection and resolution problem in air traffic management consists of deciding the best strategy for an arbitrary aircraft configuration such that all conflicts in the airspace are avoided. A conflict situation occurs if two or more aircraft do not maintain the minimum safety distance during their flight plans. A two-step approach is presented. The first step consists of a nonconvex mixed integer nonlinear optimization (MINLO) model based on geometric constructions. The objective is to minimize the weighted aircraft angle variations to obtain the new flight configuration. The second step consists of a set of unconstrained quadratic optimization models where aircraft are forced to return to their original flight plan as soon as possible once there is no aircraft in conflict with any other. The main results of extensive computation are reported by comparing the performance of state-of-the-art nonconvex MINLO solvers and an approximation by discretizing the possible angles of motion for solving a sequence of integer linear optimization (SILO) models in an iterative way. Minotaur, one of the nonconvex MINLO solvers experimented with, gives better solutions but requires more computation time than the SILO approach, which requires only a short time to obtain a good, feasible solution. Its value in the objective function has a reasonable goodness gap compared with the Minotaur solution. Given the need to solve the problem in almost real time, the approximate SILO approach is favored because of its short computation time and solution quality for the testbeds used in the experiment, which include both small- and real-sized instances. However, Minotaur is useful in this particular case for simulation purposes and for calibrating the SILO approach.