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Global optimization problems whose objective function is expensive toevaluate can be solved effectively by recursively fitting a surrogate functionto function samples and minimizing an acquisition function to generate newsamples. The acquisition step trades off between seeking for a new optimizationvector where the surrogate is minimum (exploitation of the surrogate) andlooking for regions of the feasible space that have not yet been visited andthat may potentially contain better values of the objective function(exploration of the feasible space). This paper proposes a new globaloptimization 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 takeninto account. Compared to Bayesian optimization, the proposed algorithm, thatwe call GLIS (GLobal minimum using Inverse distance weighting and Surrogateradial basis functions), is competitive and computationally lighter, as we showin 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}.

Global optimization via inverse distance weighting and radial basis functions