Chaos-enhanced metaheuristics: classification, comparison, and convergence analysis

Chaos theory, with its unique blend of randomness and ergodicity, has become a powerful tool for enhancing metaheuristic algorithms. In recent years, there has been a growing number of chaos-enhanced metaheuristic algorithms (CMAs), accompanied by a notable scarcity of studies that analyze and organize this field. To respond to this challenge, this paper comprehensively analyzes recent advances in CMAs from 2013 to 2024, proposing a novel classification scheme that systematically organizes prevalent and practical approaches for integrating chaos theory into metaheuristic algorithms based on their strategic roles. In addition, a list of 27 standard chaotic maps is explored, and a summary of the application domains where CMAs have demonstrably improved performance is provided. To experimentally demonstrate the capability of chaos theory to enhance metaheuristic algorithms that face common issues such as susceptibility to local optima, non-smooth transitions between global and local search phases, and decreased diversity, we developed a chaotic variant of the recently proposed RIME optimizer, which also encounters these challenges to some extent. We tested C-RIME on the CEC2022 benchmark suite, rigorously analyzing numerical results using statistical metrics. Non-parametric statistical tests, including the Friedman and Wilcoxon signed-rank tests, were also used to validate the findings. The results demonstrated promising performance, with 14 out of 21 chaotic variants outperforming the non-chaotic variant, whereas the piecewise map-based variant achieved the best results. In addition, C-RIME outperformed ten state-of-the-art metaheuristic algorithms regarding solution quality and convergence speed.