A two-stage metaheuristic algorithm for the multi-drops flying sidekick traveling salesman problem

In this paper, an integer programming model, based on the flight range limitation of the drone, is formulated for the multi-drops flying sidekick traveling salesman problem (mFSTSP). The connection between the mFSTSP and the corresponding traveling salesman problem (TSP) is then explored, providing a basis for solving the problem in two stages. Subsequently, a new two-stage metaheuristic algorithm is proposed. In the first stage, an adaptive large neighborhood search algorithm with the nearest neighbor operator is employed to solve the corresponding TSP. In the second stage, the obtained TSP route is segmented based on the flight range limitation of the drone, and the simulated annealing framework is used to explore the optimal node allocation scheme of each segment in sequence. Numerical experiments are conducted under varying truck-drone speed ratios and diverse drone maximum flight ranges. The experimental results indicate that optimal or near-optimal solutions to the problem can be obtained in a significantly short time. Furthermore, the proposed two-stage metaheuristic algorithm shows remarkable advantages in solving large-scale instances compared with several advanced heuristic algorithms.