# Global optimization via inverse distance weighting and radial basis functions

## TL;DR

This paper introduces GLIS, a new global optimization algorithm that combines inverse distance weighting and radial basis functions to efficiently solve expensive objective function problems, outperforming Bayesian methods in benchmarks.

## Contribution

The paper presents a novel optimization method, GLIS, that effectively integrates IDW and RBF for surrogate modeling, offering a computationally lighter alternative to Bayesian optimization.

## Key findings

- GLIS is competitive with Bayesian optimization in benchmark tests.
- GLIS handles simple constraints easily.
- The method is computationally lighter than Bayesian approaches.

## Abstract

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}.