Biobjective route planning of an unmanned air vehicle in continuous space

We consider the route planning problem of an unmanned air vehicle (UAV) in a continuous space that is monitored by radars. The UAV visits multiple targets and returns to the base. The routes are constructed considering the total distance traveled and the total radar detection threat objectives. The UAV is capable of moving to any point in the terrain. This leads to infinitely many efficient trajectories between target pairs and infinitely many efficient routes to visit all targets. We use a two stage approach in solving the complex problem of finding all efficient routes. In the first stage, we structure the nondominated frontiers of the efficient trajectories between all target pairs. For this, we first identify properties shared by efficient trajectories between target pairs that are protected by a radar. This helps to structure the nondominated frontier between any target pair by identifying at most four specific efficient trajectories. We develop a search-based algorithm that finds these efficient trajectories effectively. For the second stage, we develop a mixed integer nonlinear program that exploits the structured nondominated frontiers between target pairs to construct the efficient routes. We compare the nondominated front we generate in the continuous space with its counterpart in a terrain discretized with three different grid fidelities. The continuous space representation outperforms all discrete representations in terms of solution quality and computational times.