Global optimization using Sobol indices

TL;DR

This paper introduces a novel global optimization algorithm that leverages Sobol indices for variance-based sensitivity analysis, reducing function evaluations and efficiently optimizing costly functions under the sparsity-of-effects principle.

Contribution

The paper presents a new derivative-free optimization method inspired by LIPO, incorporating Sobol indices to improve efficiency for functions with sparse effects.

Findings

Reduces the number of objective function calls

Effective for costly functions with sparse effects

Demonstrates improved optimization efficiency

Abstract

We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method should be efficient to optimize costly functions satisfying the sparsity-of-effects principle.