Optimization of fractional-order chaotic cellular neural networks by metaheuristics

• Published in: The European physical journal. ST, Special topics Vol. 231; no. 10; pp. 2037 - 2043
• Main Authors: Tlelo-Cuautle, Esteban, González-Zapata, Astrid Maritza, Díaz-Muñoz, Jonathan Daniel, de la Fraga, Luis Gerardo, Cruz-Vega, Israel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022; Springer Nature B.V
• Subjects: Algorithms; Artificial intelligence; Artificial neural networks; Atomic; Cellular communication; Chaos theory; Chaotic Variable-Order Fractional Neural Networks; Classical and Continuum Physics; Condensed Matter Physics; Evolutionary computation; Fourier transforms; Heuristic methods; Materials Science; Measurement Science and Instrumentation; Molecular; Neural networks; Optical and Plasma Physics; Optimization; Particle swarm optimization; Physics; Physics and Astronomy; Problem solving; Regular; Regular Article; Swarm intelligence; Time series
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjs/s11734-022-00452-6

Artificial neural networks have demonstrated to be very useful in solving problems in artificial intelligence. However, in most cases, ANNs are considered integer-order models, limiting the possible applications in recent engineering problems. In addition, when dealing with fractional-order neural networks, almost any work shows cases when varying the fractional order. In this manner, we introduce the optimization of a fractional-order neural network by applying metaheuristics, namely: differential evolution (DE) and accelerated particle swarm optimization (APSO) algorithms. The case study is a chaotic cellular neural network (CNN), for which the main goal is generating fractional orders of the neurons whose Kaplan–Yorke dimension is being maximized. We propose a method based on Fourier transform to evaluate if the generated time series is chaotic or not. The solutions that do not have chaotic behavior are not passed to the time series analysis (TISEAN) software, thus saving execution time. We show the best solutions provided by DE and APSO of the attractors of the fractional-order chaotic CNNs.