  Bayesian optimization is an effective method to efficiently optimize unknown
objective functions with high evaluation costs. Traditional Bayesian
optimization algorithms select one point per iteration for single objective
function, whereas in recent years, Bayesian optimization for multi-objective
optimization or multi-point search per iteration have been proposed. However,
Bayesian optimization that can deal with them at the same time in non-heuristic
way is not known at present. We propose a Bayesian optimization algorithm that
can deal with multi-objective optimization and multi-point search at the same
time. First, we define an acquisition function that considers both
multi-objective and multi-point search problems. It is difficult to
analytically maximize the acquisition function as the computational cost is
prohibitive even when approximate calculations such as sampling approximation
are performed; therefore, we propose an accurate and computationally efficient
method for estimating gradient of the acquisition function, and develop an
algorithm for Bayesian optimization with multi-objective and multi-point
search. It is shown via numerical experiments that the performance of the
proposed method is comparable or superior to those of heuristic methods.
