Bat Algorithm gets rigorous parameter tuning via dynamical systems theory

In a new paper on arXiv, Xin-She Yang and Mehmet Karamanoglu tackle one of metaheuristics' biggest challenges: theoretical parameter setting. While the Bat Algorithm is widely used for optimization problems, its parameters have typically been tuned through trial-and-error. The authors apply dynamical systems theory and population variance evolution to derive rigorous mathematical bounds for key parameters. Their analysis shows that these theoretical ranges align closely with empirical results from numerical experiments, bridging a long-standing gap between theory and practice. The study also sheds light on how parameters influence exploration versus exploitation and overall convergence behavior.

The work is significant because it moves beyond ad-hoc tuning toward principled parameter selection. By establishing a formal connection between variance evolution and algorithm dynamics, the authors provide a framework that could be extended to other metaheuristics like particle swarm or firefly algorithms. For practitioners, this means more reliable performance without extensive manual tuning. The paper, presented at ICCS2026, includes 14 pages of analysis with 5 figures, and demonstrates that theoretical consistency is achievable in heuristic optimization.