Convergence Analysis of Swarm Intelligence Based on Fuzzy Random Variables

The particle swarm optimizer algorithm is a bio-inspired optimization principle and a typical swarm intelligence algorithm whose theory base is random theory. Many researchers attempted to make the PSO process clearly from the perspective of the random theory but got some complicated and nonobjective results. In this paper from the perspective of base theory, the fitness function that evaluates the performance of particles in the swarm is shown by a fuzzy random variable while the convergence and its speed of PSO process can be shown by the two parameters (the belief level value and the Borel set) of the chance measure of fuzzy random variable. Then we can obtain some straightforward and concrete results.