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This investigation develops an innovative algorithm for multiple autonomous unmanned aerial vehicle (UAV) mission routing. The concept of a UAV swarm routing problem (SRP) as a new combinatorics problem, is developed as a variant of the vehicle routing problem with time windows (VRPTW). Solutions of SRP problem model result in route assignments per vehicle that successfully track to all targets, on time, within distance constraints. A complexity analysis and multi-objective formulation of the VRPTW indicates the necessity of a stochastic solution approach leading to a multi-objective evolutionary algorithm. A full problem definition of the SRP as well as a multi-objective formulation parallels that of the VRPTW method. Benchmark problems for the VRPTW are modified in order to create SRP benchmarks. The solutions show the SRP solutions are comparable or better than the same VRPTW solutions, while also representing a more realistic UAV swarm routing solution.