Swarm Intelligence and Bio-Inspired Computation: 6. Particle Swarm Algorithm: Convergence and Applications

In this chapter, we present the convergence analysis and applications of particle swarm optimization algorithm. Although it is difficult to analyze the convergence of this algorithm, we discuss its convergence based on its iterated function system and probabilistic theory. The dynamic trajectory of the particle is described based on single individual. We also attempt to theoretically prove that the swarm algorithm converges with a probability of 1 toward the global optimal. We apply the algorithms to solve the scheduling problem and peer-to-peer neighbor selection problem. This chapter is also concerned to employ the nature-inspired optimization methods in machine learning. We introduce the swarm algorithm to reoptimize hidden Markov models.