This paper studies an unmanned aerial vehicle (UAV)-assisted wireless network, where a UAV is dispatched to gather information from ground sensor nodes (SN) and transfer the collected data to the depot. The information freshness is captured by the age of information (AoI) metric, whilst the energy consumption of the UAV is seen as another performance criterion. Most importantly, the AoI and energy efficiency are inherently competing metrics, since decreasing the AoI requires the UAV returning to the depot more frequently, leading to a higher energy consumption. To this end, we design UAV paths that optimize these two competing metrics and reveal the Pareto frontier. To formulate this problem, a multi-objective mixed integer linear programming (MILP) is proposed with a flow-based constraint set and we apply Benders decomposition on the proposed formulation. The overall outcome shows that the proposed method allows deriving non-dominated solutions for decision making for UAV based wireless data collection. Numerical results are provided to corroborate our study by presenting the Pareto front of the two objectives and the effect on the UAV trajectory.
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