This paper investigates the problem of route planning for rechargeable unmanned aerial vehicles (UAV) under the mission time constraint in cases where more than one trip per round is required due to limited battery capacities. The goal is to determine the number of UAVs to be deployed and the flying paths that minimize the total mission cost. Unlike previous works, the electric cost incurred by UAV recharging proportional to actual flying distances is incorporated into our model. The problem is formulated as a mixed-integer programming model to minimize the sum of electric charging cost, the UAV usage cost, and the penalty cost from the violation of the mission time constraint. Extensive numerical experiments are conducted to examine the integrity and performance of the proposed model under various model parameters and deployment scenarios in grid areas and a real terrain area. The optimal solutions can be obtained for small-scale problem instances in a reasonable runtime. For large-scale problems, only feasible solutions can be obtained due to limited computational resources.

Purpose: We consider the problem of route planning of multiple rechargeable heterogeneous UAVs with multiple trips under mission time and payload carrying constraints. The goal is to determine the types and number of UAVs to be deployed and their flying paths that minimizes the monetary cost, which is a sum of the recharging energy cost of each UAV, the UAV rental cost, and the cost of violating the mission time deadline.Design/methodology/approach: The problem is formulated as a mixed integer programming (MIP). Then, the genetic algorithm (GA) is developed to solve the model and the solutions are compared to those obtained from the exact method (Branch-and-Bound). Novel chromosome encoding and population initializations are designed, and standard procedures for crossover and mutation are adapted to this work. Test problems on grid networks and real terrains are used to evaluate the runtime efficiency and solution optimality, and the sensitivity of GA parameters is studied based on two-level factorial experiments.Findings: The proposed GA method can find optimal solutions for small problem sizes but with much less computation time than the exact method. For larger problem sizes, the exact method failed to find optimal solutions within the limits of time and disk space constraints (24 hours and 500 GB) while the GA method yields the solutions within a few minutes with as high as 49% better objective values. Also, the proposed GA method is shown to well explore the solution space based on the variation of the total costs obtained.Originality/value: The unique aspects of this work are that the model optimizes the sum of three different costs – the electricity recharging cost, the UAV rental cost, the penalty cost for mission deadline violation, and the recharging period based on the remaining energy, the payload capacity, and the heterogeneity of UAVs are incorporated into the model. The model is formulated as a mixed integer programming and the genetic algorithm is developed to solve the program. Novel chromosome encoding and population initializations are designed, and standard procedures for crossover and mutation are adapted to this work.