PSO Advances and Application to Inverse Problems

Particle swarm optimization (PSO) is a Swarm Intelligence technique used for optimization motivated by the social behavior of individuals in large groups in nature. The damped mass-spring analogy known as the PSO continuous model allowed us to derive a whole family of particle swarm optimizers with different properties with regard to their exploitation/exploration balance. Using the theory of stochastic differential and difference equations, we fully characterize the stability behavior of these algorithms. PSO and RR-PSO are the most performant algorithms of this family in terms of rate of convergence. Other family members have better exploration capabilities. The so called four point algorithms use more information of previous iterations to update the particles positions and trajectories and seem to be more exploratory than most of the 3 points versions. Finally, based on the done analysis, we can affirm that the PSO optimizers are not heuristic algorithms since there exist mathematical results that can be used to explain their consistency/convergence.