A Granular Sieving Algorithm for Deterministic Global Optimization

TL;DR

This paper introduces a gradient-free, deterministic algorithm for global optimization of Lipschitz functions, utilizing a granular sieving approach to efficiently locate global minima in arbitrary compact sets.

Contribution

The paper presents a novel granular sieving algorithm that deterministically finds global minima for Lipschitz functions in arbitrary compact sets, applicable to both univariate and multivariate cases.

Findings

Effective in locating global minima in benchmark tests

Applicable to both univariate and multivariate functions

Demonstrates computational efficiency and robustness

Abstract

A gradient-free deterministic method is developed to solve global optimization problems for Lipschitz continuous functions defined in arbitrary path-wise connected compact sets in Euclidean spaces. The method can be regarded as granular sieving with synchronous analysis in both the domain and range of the objective function. With straightforward mathematical formulation applicable to both univariate and multivariate objective functions, the global minimum value and all the global minimizers are located through two decreasing sequences of compact sets in, respectively, the domain and range spaces. The algorithm is easy to implement with moderate computational cost. The method is tested against extensive benchmark functions in the literature. The experimental results show remarkable effectiveness and applicability of the algorithm.