Critical Parameters in Particle Swarm Optimisation
This work provides theoretical insights into PSO parameter tuning, which is incremental but useful for researchers and practitioners in optimization.
The study analyzed particle swarm optimization (PSO) using random dynamical systems to derive analytical stability conditions, identifying a critical parameter relationship that separates convergent and divergent behaviors, with simulations showing optimal performance near this instability margin.
Particle swarm optimisation is a metaheuristic algorithm which finds reasonable solutions in a wide range of applied problems if suitable parameters are used. We study the properties of the algorithm in the framework of random dynamical systems which, due to the quasi-linear swarm dynamics, yields analytical results for the stability properties of the particles. Such considerations predict a relationship between the parameters of the algorithm that marks the edge between convergent and divergent behaviours. Comparison with simulations indicates that the algorithm performs best near this margin of instability.