Convergence analysis of swarm algorithm

Swarm Intelligence (SI) is an innovative distributed intelligent paradigm whereby the collective behaviors of unsophisticated individuals interacting locally with their environment cause coherent functional global patterns to emerge. Although the swarm algorithms have exhibited good performance across a wide range of application problems, it is difficult to analyze the convergence. We discuss the swarm intelligent model namely the particle swarm based on its iterated function system. The dynamic trajectory of the particle is described based single individual. We also attempt to theoretically prove that the swarm algorithm converges with a probability of 1 towards the global optimal.