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The Drone Routing Problem with Energy replenishment (DRP-E) belongs to ageneral class of routing problems with intermediate stops and synchronizationconstraints. In DRP-E, the drone has to visit a set of nodes and routinelyrequires battery swaps from a (potentially) mobile replenishment station.Contrary to widespread restrictions in the drone routing literature, severaldestinations may be visited in between two consecutive battery swaps. In thispaper, we propose a nontrivial very large-scale neighbourhood for DRP-E, whichsynergetically leverages two large-sized polynomially solvable DRP-ESubProblems (SP1 and SP2). The number of feasible solutions in the resultingneighborhood is a multiple of those in SP1 and SP2, and, thus, exponential inthe input size of the problem, whereas the computational time to search itremains polynomial. The proposed polynomial two-stage dynamic programmingalgorithm VLSN to search this neighborhood can be flexibly adjusted to thedesired trade-off between accuracy and computational time. For instance, thesearch procedure can be converted into an exact algorithm of competitiveruntime for DRP-E. In computational tests, the developed solution methodsoutperform current state-of-the art heuristics for DRP-E by a significantmargin. A case study based on a search for missing persons demonstrates thatVLSN easily accommodates additional practice relevant features and outperformsthe state-of-the-art solution in disaster relief by 20%.

Very large-scale neighborhood search for drone routing with energy replenishment