  The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem
(NPO) that has been of great interest for decades for both, science and
industry. The CVRP is a variant of the vehicle routing problem characterized by
capacity constrained vehicles. The aim is to plan tours for vehicles to supply
a given number of customers as efficiently as possible. The problem is the
combinatorial explosion of possible solutions, which increases
superexponentially with the number of customers. Classical solutions provide
good approximations to the globally optimal solution. D-Wave's quantum annealer
is a machine designed to solve optimization problems. This machine uses quantum
effects to speed up computation time compared to classic computers. The problem
on solving the CVRP on the quantum annealer is the particular formulation of
the optimization problem. For this, it has to be mapped onto a quadratic
unconstrained binary optimization (QUBO) problem. Complex optimization problems
such as the CVRP can be translated to smaller subproblems and thus enable a
sequential solution of the partitioned problem. This work presents a
quantum-classic hybrid solution method for the CVRP. It clarifies whether the
implemenation of such a method pays off in comparison to existing classical
solution methods regarding computation time and solution quality. Several
approaches to solving the CVRP are elaborated, the arising problems are
discussed, and the results are evaluated in terms of solution quality and
computation time.
