The sad state of self-adaptive particle swarm optimizers

The performance of the Particle Swarm Optimization (PSO) algorithm can be greatly improved if the parameters are appropriately tuned. However, tuning the control parameters for PSO algorithms has traditionally been a time-consuming, empirical process. Furthermore, ideal parameters may be time-dependent. To address the issue of parameter tuning, self-adaptive PSO (SAPSO) algorithms adapt the PSO control parameters over time. While many such SAPSO techniques have been proposed, their behaviour is not well understood as no in-depth critical analysis of their adaptation mechanisms has been performed. This study examines the convergence behaviour of eight SAPSO algorithms both analytically and empirically. Evidence clearly indicates that the field of self-adaptive PSO algorithms is in a sad state, given that many techniques either demonstrate divergent behaviour coupled with excessive invalid particles, and thus infeasible solutions, or have prohibitively low particle step sizes caused by rapid convergence.