Stability analysis of the particle dynamics in bat algorithm: standard and modified versions

Stability and convergence analysis have been previously accomplished for some population-based search and swarm intelligence algorithms like Particle Swarm Optimization and Gravitational Search Algorithm. However, there is no adequate theoretical analysis for Bat Algorithm (BA) in the literature. The BA is a type of optimization algorithms which is inspired by the motion of small bats searching for hunting their preys. In this study, stability and convergence of the particle dynamics in the standard version BA are analyzed, and some restrictions are described. Then, new updating relations have been proposed. Also the dynamics of the algorithm have been investigated, and sufficient conditions for stability have been derived using Lyapunov stability analysis. Extensive simulation is used to examine the findings. The results confirm the theoretical predictions and indicate the stability and convergence of the proposed updating relations.