# MRF–PSO–MultiRoot Finding Particle Swarm Optimization Algorithm for Nonlinear Functions

## Abstract

Finding approximations to the zeros or roots of nonlinear functions is a task that is often required in various applications in different fields of science and engineering. Although there are many iterative methods that can be used for finding such roots, they typically need good initial approximations to converge, and a number of them also demand the computation of derivatives, which is not always possible and in addition can be computationally intensive, or even request repeated deflations or many algorithm runs with different initial guesses for finding all roots. Finding roots of systems of nonlinear functions is an even more complex problem. This paper presents a novel variant of the particle swarm optimization algorithm for root finding aiming to surpass these drawbacks. The MultiRoot Finding Particle Swarm Optimization (MRF–PSO) algorithm here proposed uses multiple swarms for exploring the space of solutions and simultaneously find approximations for the different single or multiple roots of a given nonlinear function. An architecture for information sharing, a technique for detecting equal roots within a given tolerance, and an intelligent particle positioning strategy are also suggested. The proposed algorithm was tested with a set of nonlinear functions, and the results obtained were compared with others available in the literature. Results revealed that the MRF–PSO algorithm constitutes an effective approach for root finding and can be certainly exploited in real-world problems from science and engineering.

Authors
Diogo Freitas; Luiz Guerreiro Lopes; Fernando Morgado-Dias
Date
2021
Conference
International Conference on Sustainable and Innovative Solutions for Current Challenges in Engineering & Technology (ICSISCET)
Publisher
Springer Nature Singapore
Conference location
Singapore (held remotely)
Source

## Citation

@inproceedings{freitas2021,
author = {Freitas, Diogo and Lopes, Luiz Guerreiro and Morgado-Dias, Fernando},
doi = {10.1007/978-981-19-1653-3_32},
booktitle = {Artificial Intelligence and Sustainable Computing},
month = {11},
pages = {423--439},
title = {MRF--PSO: MultiRoot finding particle swarm optimization algorithm for nonlinear functions},
year = {2021}
}