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Hybridization of Nonlinear and Mixed-Integer Linear Programming for Aircraft Separation With Trajectory Recovery

The approach presented in this paper aims at finding a solution to the problem of conflict-free motion planning for multiple aircraft on the same flight level with trajectory recovery. One contribution of this work is to develop three consistent models, i.e., from a continuous-time representation to a discrete-time linear approximation. Each of these models guarantees separation at all times and trajectory recovery, but they are not equally difficult to solve. A new hybrid algorithm is thus developed to use the optimal solution of a mixed-integer linear program as a starting point when solving a nonlinear formulation of the problem. The significance of this process is that it always finds a solution when the linear model is feasible while still taking into account the nonlinear nature of the problem. A test bed containing numerous data sets is then generated from three virtual scenarios. A comparative analysis with three different initializations of nonlinear optimization validates the efficiency of the hybrid method.