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Artificial Intelligence and Sustainable Computing pp 423–439Cite as

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

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Part of the Algorithms for Intelligent Systems book series (AIS)

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.

Keywords

  • Computational intelligence
  • Particle swarm optimization
  • Root finding
  • Nonlinear functions
  • Nonlinear systems

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Acknowledgements

This work was supported by the Project MITIExcell (Project—UIDB/50009/ 2020), co-financed by Regional Development European Funds for the “Operational Program Madeira 14–20”—Priority Axis 1 of the Autonomous Region of Madeira, Number M1420-01-0145-FEDER-000002. In addition, the funding from LARSyS–FCT Pluriannual funding 2020–2023 is acknowledged.

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Authors and Affiliations

  1. Madeira Interactive Technologies Institute (ITI/LARSyS/M-ITI), 9020-105, Funchal, Portugal

    Diogo Nuno Freitas & Fernando Morgado-Dias

  2. NOVA Laboratory for Computer Science and Informatics (NOVA LINCS), 2829-516, Caparica, Portugal

    Diogo Nuno Freitas

  3. Faculty of Exact Sciences and Engineering, University of Madeira, 9020-105 Funchal, Madeira Is., Funchal, Portugal

    Diogo Nuno Freitas, Luiz Guerreiro Lopes & Fernando Morgado-Dias

Authors
  1. Diogo Nuno Freitas
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  2. Luiz Guerreiro Lopes
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  3. Fernando Morgado-Dias
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Corresponding author

Correspondence to Diogo Nuno Freitas .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Madhav Institute of Technology and Science, Gwalior, India

    Manjaree Pandit

  2. Madhav Institute of Technology and Science, Gwalior, India

    M. K. Gaur

  3. Thapar Institute of Engineering and Technology, Patiala, India

    Prashant Singh Rana

  4. Madhav Institute of Technology and Science, Gwalior, India

    Akhilesh Tiwari

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Freitas, D.N., Lopes, L.G., Morgado-Dias, F. (2022). MRF–PSO: MultiRoot Finding Particle Swarm Optimization Algorithm for Nonlinear Functions. In: Pandit, M., Gaur, M.K., Rana, P.S., Tiwari, A. (eds) Artificial Intelligence and Sustainable Computing. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-19-1653-3_32

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