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The problem of designing optimal conflict-free maneuvers for planar multiple aircraft encounters is studied. The maneuvers propose suitable heading changes for aircraft in a cooperative manner. The new mathematical approach provides optimal aircraft trajectories to resolve a wide variety of conflicts, especially in the presence of high-altitude clear air turbulence (CAT), normally encountered during en-route flights. The proposed approach effectively uses Genetic Algorithms (GA), together with modified webs, to quickly find conflict-resolving maneuvers. Different case studies show the method is fast enough to be used for real-time applications when resolving conflicts involving two aircraft. It is also efficient enough to resolve conflicts involving as many as 26 aircraft, which would be helpful in designing acrobatic maneuvers or in congested airspaces where emergency plans are needed.