IPAB workshop - Michael Herrmann - Critical Particle Swarms for Optimization and Exploration

Particle swarm optimization is a metaheuristic algorithm that was inspired by the flocking behaviour of birds and schooling of fish. It has been proposed to find reasonable solutions in a wide range of applied problems. 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. This analysis goes beyond existing approaches that were restricted to trivialised versions of the algorithm as it addresses the crucial effect of the stochasticity of the algorithm and its usefulness in applications to optimisation problems. Comparison with simulations confirms that the algorithm performs best near the margin of instability. The second part of the talk will discuss implications for other metaheuristic algorithms and applications in robotics.