Stability Analysis of Bat Algorithm

Bat Algorithm is a type of swarm intelligence algorithm which is inspired by the behavior of little bats which are looking for direction in hunting opportunities. Swarm intelligence algorithms are inspired by the nature which are very efficient on crucial optimization problems. These algorithms are simple, flexible and can be implemented easily as well. Analyzing swarm intelligence algorithms makes their utilization reliable and guarantees finding answers by them. Earlier, stability analysis has been accomplished for some swarm intelligence algorithms including Particle Swarm Optimization and Gravitational Search but sufficient mathematical analysis for the bat algorithm has not been done. For this purpose, in the present paper, we considered Bat Algorithm stability analysis using Lyapunov method. In this study, at first, stability analysis of standard bat algorithm has been analyzed. Because of unsuccessful attempts to analyze the stability of standard algorithm, new updating relations has been introduced to increase the degree of freedom. The stability analysis has been presented for these relations. Experimental results illustrate the stability of the new updating relations.