Chaotic attractors of discrete dynamical systems used in the core of evolutionary algorithms: state of art and perspectives

Abstract

This paper delves into the intersection between discrete dynamical systems and bio-inspired metaheuristic algorithms. Chaos, an inherent phenomenon manifested by both continuous and discrete dynamic nonlinear systems has become an essential component of engineering design. This study examines the relationship between chaos and bio-inspired metaheuristic algorithms from two distinct angles: the presence of chaos within the realm of algorithms, and the application of bio-inspired algorithms for the identification, control, or synthesis of complex systems. Furthermore, this paper offers an in-depth exploration of the interplay between metaheuristics and complex nonlinear dynamics, including potential avenues for future research. The presented simulation studies, along with the design of objective functions for optimization and the implementation of metaheuristics, serve as a valuable foundation for subsequent experiments involving discrete nonlinear systems and complex systems with time delays. Such systems may benefit from multiparametric or multicriteria optimization approaches, paving the way for novel advancements in the field.

Keywords:

• Deterministic chaos
• metaheuristics
• evolution algorithms
• swarm intelligence
• discrete chaotic dynamical systems
• chaotic maps

Mathematical Subject classifications:

• 34H10
• 35Q93
• 68T20
• 68W50

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by a grant of SGS No. SP2023/050, VSB-Technical University of Ostrava, Czech Republic, by the Grant Agency of Czech Republic (GACR) project No. GF21-45465L, and further by the resources of A.I.Lab at the Faculty of Applied Informatics, Tomas Bata University in Zlin.