Konvergenzanalyse für die Partikelschwarmoptimierung
- Manuel Schmitt
- Ausgezeichnete Informatikdissertationen
Particle swarm optimization (PSO) is an optimization approach from the field of artificial intelligence. A population of so-called particles moves through the parameter space defined by the optimization problem, searching for good solutions. Inspired by natural swarms, the movements of the swarm members depend on own experiences and on the experiences of adjacent particles. PSO algorithms are mainly used for continuous optimization problems, whose feasible space is often restricted by a set of constraints. A special case are box constraints, which define upper and lower bounds for the problem parameters. In the literature, there exist several so-called bound handling strategies to integrate box constraints in PSO algorithms, such as setting infeasible particles to the nearest feasible position or reflecting them at the boundary. In this thesis, various aspects of box-constrained particle swarm optimization are examined. The core of this work is the theoretical analysis of the impact of box constraints for particle swarm optimization. It is shown mathematically that initial particle swarm performance strongly depends on the chosen bound handling strategy due to the fact that, with overwhelming probability, many particles leave the feasible space at the beginning of the optimization. Moreover, by using a simplified PSO model, is shown that this effect can be reduced if particle velocities are scaled with respect to the problem dimensionality. A thorough experimental evaluation shows that bound handling also significantly influences the final solution quality of a particle swarm optimizer, especially when applied to high-dimensional problems. Three way to cope with these results in practical PSO applications are presented: The careful selection of bound handling strategies, the use of self-adaptation, and the use of velocity adaptation. Finally, the investigated PSO algorithms are applied to an optimization problem from the field of mechanical engineering.