How can evolutionary algorithms adapt to changing landscapes? This paper presents a theoretical analysis of mutation-adaptive evolutionary algorithms, emphasizing the need for sophisticated modeling techniques to understand their dynamic behavior. The authors account for the complete history of the algorithm's evolution, moving beyond the limitations of Markov chains by using random systems with complete connections. The study enhances the understanding of the inner workings and adaptive capabilities of evolutionary algorithms. The analysis covers several mutation-adaptive algorithms: a binary genetic algorithm, the 1/5 success rule evolution strategy, and continuous and dynamic (1+1) evolutionary algorithms. The new paradigm of random systems with complete connections enables a more accurate representation of the complex dynamics involved in adaptation. This research has implications for the design and optimization of adaptive algorithms in various fields, including computer science, engineering, and optimization. By providing a theoretical framework for analyzing their convergence and behavior, this work contributes to the development of more robust and efficient evolutionary algorithms.
Published in Evolutionary Computation, this paper aligns with the journal's focus on theoretical foundations and practical applications of evolutionary algorithms. It addresses a key challenge in the field—parameter adaptation—and provides a rigorous analysis of various adaptive strategies, significant to the journal's audience.