  The Drone Routing Problem with Energy replenishment (DRP-E) belongs to a
general class of routing problems with intermediate stops and synchronization
constraints. In DRP-E, the drone has to visit a set of nodes and routinely
requires battery swaps from a (potentially) mobile replenishment station.
Contrary to widespread restrictions in the drone routing literature, several
destinations may be visited in between two consecutive battery swaps. In this
paper, we propose a nontrivial very large-scale neighbourhood for DRP-E, which
synergetically leverages two large-sized polynomially solvable DRP-E
SubProblems (SP1 and SP2). The number of feasible solutions in the resulting
neighborhood is a multiple of those in SP1 and SP2, and, thus, exponential in
the input size of the problem, whereas the computational time to search it
remains polynomial. The proposed polynomial two-stage dynamic programming
algorithm VLSN to search this neighborhood can be flexibly adjusted to the
desired trade-off between accuracy and computational time. For instance, the
search procedure can be converted into an exact algorithm of competitive
runtime for DRP-E. In computational tests, the developed solution methods
outperform current state-of-the art heuristics for DRP-E by a significant
margin. A case study based on a search for missing persons demonstrates that
VLSN easily accommodates additional practice relevant features and outperforms
the state-of-the-art solution in disaster relief by 20%.
