Convergence analysis and empirical research of the sparrow search algorithm

This paper delves into the convergence of the Sparrow Search Algorithm (SSA) and constructs a rigorous proof system based on Markov chain theory. Through detailed mathematical derivations, it demonstrates the ergodicity of the algorithm, the existence of a stationary distribution, and its convergence to the global optimal solution. The complete calculation steps and implementation code of the algorithm are provided, and numerical experiments are carried out to comprehensively evaluate the algorithm's performance. Abundant data is presented to verify the correctness of the theoretical analysis, providing a solid theoretical and practical support for the wide application of SSA. Meanwhile, innovative approaches to high-dimensional problems and dynamic environments are proposed, laying the foundation for the future development of the algorithm.