Dynamical Sphere Regrouping Particle Swarm Optimization Programming: An Automatic Programming Algorithm Avoiding Premature Convergence

Martín Montes Rivera (), Carlos Guerrero-Mendez (), Daniela Lopez-Betancur and Tonatiuh Saucedo-Anaya
Additional contact information
Martín Montes Rivera: Unidad Académica de Ciencia y Tecnología de la Luz y la Materia, Universidad Autónoma de Zacatecas, Campus es Parque de Ciencia y Tecnología QUANTUM, Cto., Marie Curie S/N, Zacatecas 98160, Mexico
Carlos Guerrero-Mendez: Unidad Académica de Ciencia y Tecnología de la Luz y la Materia, Universidad Autónoma de Zacatecas, Campus es Parque de Ciencia y Tecnología QUANTUM, Cto., Marie Curie S/N, Zacatecas 98160, Mexico
Daniela Lopez-Betancur: Unidad Académica de Ciencia y Tecnología de la Luz y la Materia, Universidad Autónoma de Zacatecas, Campus es Parque de Ciencia y Tecnología QUANTUM, Cto., Marie Curie S/N, Zacatecas 98160, Mexico
Tonatiuh Saucedo-Anaya: Unidad Académica de Ciencia y Tecnología de la Luz y la Materia, Universidad Autónoma de Zacatecas, Campus es Parque de Ciencia y Tecnología QUANTUM, Cto., Marie Curie S/N, Zacatecas 98160, Mexico

Mathematics, 2024, vol. 12, issue 19, 1-53

Abstract: Symbolic regression plays a crucial role in machine learning and data science by allowing the extraction of meaningful mathematical models directly from data without imposing a specific structure. This level of adaptability is especially beneficial in scientific and engineering fields, where comprehending and articulating the underlying data relationships is just as important as making accurate predictions. Genetic Programming (GP) has been extensively utilized for symbolic regression and has demonstrated remarkable success in diverse domains. However, GP’s heavy reliance on evolutionary mechanisms makes it computationally intensive and challenging to handle. On the other hand, Particle Swarm Optimization (PSO) has demonstrated remarkable performance in numerical optimization with parallelism, simplicity, and rapid convergence. These attributes position PSO as a compelling option for Automatic Programming (AP), which focuses on the automatic generation of programs or mathematical models. Particle Swarm Programming (PSP) has emerged as an alternative to Genetic Programming (GP), with a specific emphasis on harnessing the efficiency of PSO for symbolic regression. However, PSP remains unsolved due to the high-dimensional search spaces and local optimal regions in AP, where traditional PSO can encounter issues such as premature convergence and stagnation. To tackle these challenges, we introduce Dynamical Sphere Regrouping PSO Programming (DSRegPSOP), an innovative PSP implementation that integrates DSRegPSO’s dynamical sphere regrouping and momentum conservation mechanisms. DSRegPSOP is specifically developed to deal with large-scale, high-dimensional search spaces featuring numerous local optima, thus proving effective behavior for symbolic regression tasks. We assess DSRegPSOP by generating 10 mathematical expressions for mapping points from functions with varying complexity, including noise in position and cost evaluation. Moreover, we also evaluate its performance using real-world datasets. Our results show that DSRegPSOP effectively addresses the shortcomings of PSO in PSP by producing mathematical models entirely generated by AP that achieve accuracy similar to other machine learning algorithms optimized for regression tasks involving numerical structures. Additionally, DSRegPSOP combines the benefits of symbolic regression with the efficiency of PSO.

Keywords: automatic programming; symbolic regression; particle swarm programming; particle swarm optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3021/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3021/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3021-:d:1487564

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().