Chaos and Swarm Intelligence

Swarm Intelligence (SI) is an innovative distributed intelligent paradigm whereby the collective behaviors of unsophisticated individuals interacting locally with their environment causing coherent functional global patterns to emerge. The intelligence emerges from a chaotic balance between individuality and sociality. The chaotic balances are a characteristic feature of the complex system. This chapter investigates the chaotic dynamic characteristics in swarm intelligence. The swarm intelligent model namely the Particle Swarm Optimization (PSO) algorithm is represented as an Iterated Function System (IFS). The dynamic trajectory of the particle is sensitive on the parameter values of IFS. The Lyapunov exponent and the correlation dimension are calculated and analyzed numerically for the dynamic system. Convergence of the swarm model is also analyzed. Our research findings illustrate that the performance of the swarm intelligent model depends on the sign of the maximum Lyapunov exponent. The particle swarm with a high maximum Lyapunov exponent usually achieves better performance, especially for multi-modal functions. The research would be helpful to parameter selection and algorithm improvements for the swarm intelligence applications.