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.

协同蝙蝠搜索算法 (CBA) 是原始蝙蝠搜索算法 (BA) 的最近开发的变体，在更新方程中具有集体速度项。数值评估已经证明了BA的优越改进。然而，仍然需要对 CBA 的理论理解，因此在本文中，使用半稳定和副收缩理论的最新成果研究了协作蝙蝠搜索算法 (CBA) 的收敛性。详细地，蝙蝠的动力学被公式化为不需要停滞假设的离散时间切换线性系统。讨论了 CBA 和原始 BA 的稳定性问题，并导出了收敛条件。而且，该算法的性能由具有六种不同响应的二阶系统的瞬态响应来解释：稳定系统的过阻尼响应、临界阻尼响应、欠阻尼响应和无阻尼响应、指数行为和不稳定系统的振荡行为。最后，通过数值评估测试CBA在不同瞬态响应下的性能，为CBA的参数选择提供更好的性能。