Unmanned aerial vehicles (UAVs) have been used extensively for search and rescue operations, surveillance, disaster monitoring, attacking terrorists, etc. due to their growing advantages of low-cost, high maneuverability, and easy deployability. This study proposes a mixed-integer programming model under a multi-objective optimization framework to design trajectories that enable a set of UAVs to execute surveillance tasks. The first objective maximizes the cumulative probability of target detection to aim for mission planning success. The second objective ensures minimization of cumulative path length to provide a higher resource utilization goal. A two-step variable neighborhood search (VNS) algorithm is offered, which addresses the combinatorial optimization issue for determining the near-optimal sequence for cell visiting to reach the target. Numerical experiments and simulation results are evaluated in numerous benchmark instances. Results demonstrate that the proposed approach can favorably support practical deployability purposes
