On the convergence of a cooperative bat searching algorithm

Abstract

The cooperative bat searching algorithm(CBA) is a recently developed variant of the original bat searching algorithm(BA) with a collective velocity term in the update equation. Numerical evaluations have demonstrated the superior improvement of BA. However, the theoretical understanding of the CBA is still needed, therefore in this paper, the convergence of a cooperative bat searching algorithm(CBA) is studied using recently developed results in semistability and paracontraction theories. In detail, the dynamics of the bats is formulated as a discrete-time switched linear system which dose not require the stagnation assumption. The CBA and the original BA’s stability issues are discussed, and the conditions of convergence are derived. Moreover, the algorithm’s performance is explained by the transient response of a second-order system with six different responses: over-damped response, critically damped response, underdamped response, and undamped response for the stable systems, exponential behavior, and oscillation behavior for unstable systems. In the end, numerical evaluation is conducted to test the performance of the CBA with different transient responses to provide parameter selections of the CBA for better performance.