  There are emerging transportation problems known as the Traveling Salesman
Problem with Drone (TSPD) and the Flying Sidekick Traveling Salesman Problem
(FSTSP) that involve using a drone in conjunction with a truck for package
delivery. This study presents a hybrid genetic algorithm for solving TSPD and
FSTSP by incorporating local search and dynamic programming. Similar algorithms
exist in the literature. Our algorithm, however, considers more sophisticated
chromosomes and less computationally complex dynamic programming to enable
broader exploration by the genetic algorithm and efficient exploitation through
dynamic programming and local search. The key contribution of this paper is the
discovery of how decision-making processes for solving TSPD and FSTSP should be
divided among the layers of genetic algorithm, dynamic programming, and local
search. In particular, our genetic algorithm generates the truck and the drone
sequences separately and encodes them in a type-aware chromosome, wherein each
customer is assigned to either the truck or the drone. We apply local search to
each chromosome, which is decoded by dynamic programming for fitness
evaluation. Our new algorithm is shown to outperform existing algorithms on
most benchmark instances in both quality and time. Our algorithms found the new
best solutions for 538 TSPD instances out of 920 and 74 FSTSP instances out of
132.
