  Global optimization problems whose objective function is expensive to
evaluate can be solved effectively by recursively fitting a surrogate function
to function samples and minimizing an acquisition function to generate new
samples. The acquisition step trades off between seeking for a new optimization
vector where the surrogate is minimum (exploitation of the surrogate) and
looking for regions of the feasible space that have not yet been visited and
that may potentially contain better values of the objective function
(exploration of the feasible space). This paper proposes a new global
optimization algorithm that uses a combination of inverse distance weighting
(IDW) and radial basis functions (RBF) to construct the acquisition function.
Rather arbitrary constraints that are simple to evaluate can be easily taken
into account. Compared to Bayesian optimization, the proposed algorithm, that
we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate
radial basis functions), is competitive and computationally lighter, as we show
in a set of benchmark global optimization and hyperparameter tuning problems.
MATLAB and Python implementations of GLIS are available at
\url{http://cse.lab.imtlucca.it/~bemporad/glis}.
