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In this paper, optimal resolution of air-traffic (AT) conflicts were considered. Aircraft are assumed to cruise within a free altitude layer and are modeled in three dimensions with variable velocity and proximity bounds. Aircraft cannot get closer to each other than a predefined safety distance. The problem of solving conflicts arising among several aircraft that are assumed to move in a shared airspace were considered. For such systems of multiple aircraft, the total flight time by avoiding all possible conflicts were minimized. This paper proposes a formulation of the conflict avoidance problem as a mixed-integer nonlinear-programming problem. In the author's case, only velocity changes are admissible as maneuvers. Nevertheless, in subsequent work, simultaneous velocity and heading angle changes will be checked too. Simulation results for realistic aircraft conflict scenarios are provided.