L\'evy flights as an underlying mechanism for global optimization algorithms

TL;DR

This paper advocates using Lévy flights as a core mechanism in stochastic optimization algorithms, enabling effective exploration of search spaces through controllable step lengths.

Contribution

It introduces Lévy flights as a novel underlying mechanism for optimization algorithms, emphasizing their ability to generate diverse step sizes for improved search efficiency.

Findings

Lévy flights facilitate better exploration in optimization.

A simple FORTRAN implementation of Lévy distribution is provided.

The method's physical basis is discussed.

Abstract

In this paper we propose and advocate the use of the so called L\'evy flights as a driving mechanism for a class of stochastic optimization computations. This proposal, for some reasons overlooked until now, is - in author's opinion - very appropriate to satisfy the need for algorithm, which is capable of generating trial steps of very different length in the search space. The required balance between short and long steps can be easily and fully controlled. A simple example of approximated L\'evy distribution, implemented in FORTRAN 77, is given. We also discuss the physical grounds of presented methods.