  In a near future drones are likely to become a viable way of distributing
parcels in a urban environment. In this paper we consider the parallel drone
scheduling traveling salesman problem, where a set of customers requiring a
delivery is split between a truck and a fleet of drones, with the aim of
minimizing the total time required to service all the customers.
  We present a set of matheuristic methods for the problem. The new approaches
are validated via an experimental campaign on two sets of benchmarks available
in the literature. It is shown that the approaches we propose perform very well
on small/medium size instances. Solving a mixed integer linear programming
model to optimality leads to the first optimality proof for all the instances
with 20 customers considered, while the heuristics are shown to be fast and
effective on the same dataset. When considering larger instances with 48 to 229
customers, the results are competitive with state-of-the-art methods and lead
to 28 new best known solutions out of the 90 instances considered.
