  Black-box optimization minimizes an objective function without derivatives or
explicit forms. Such an optimization method with continuous variables has been
successful in the fields of machine learning and material science. For discrete
variables, the Bayesian optimization of combinatorial structure (BOCS) is a
powerful tool for solving black-box optimization problems. A surrogate model
used in BOCS is the quadratic unconstrained binary optimization (QUBO) form.
Because of the approximation of the objective function to the QUBO form in
BOCS, BOCS can expand the possibilities of using D-Wave quantum annealers,
which can generate near-optimal solutions of QUBO problems by utilizing quantum
fluctuation. We demonstrate the use of BOCS and its variant for a vehicle
design problem, which cannot be described in the QUBO form. As a result, BOCS
and its variant slightly outperform the random search, which randomly
calculates the objective function.
