  A frequent starting point of quantum computation platforms are two-state
quantum systems, i.e., qubits. However, in the context of integer optimization
problems, relevant to scheduling optimization and operations research, it is
often more resource-efficient to employ quantum systems with more than two
basis states, so-called qudits. Here, we discuss the quantum approximate
optimization algorithm (QAOA) for qudit systems. We illustrate how the QAOA can
be used to formulate a variety of integer optimization problems such as graph
coloring problems or electric vehicle (EV) charging optimization. In addition,
we comment on the implementation of constraints and describe three methods to
include these into a quantum circuit of a QAOA by penalty contributions to the
cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical
decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present
numerical results for a charging optimization problem mapped onto a
max-$k$-graph coloring problem. Our work illustrates the flexibility of qudit
systems to solve integer optimization problems.
