An Analysis of Particle Swarm Optimizers by Frans van den Bergh This thesis presents a theoretical model to describe the long-term behavior of the Particle Swarm Optimizer (PSO) algorithm. An enhanced version of the PSO is constructed and shown to have guaranteed convergence on local minima. This algorithm is extended further, resulting in an algorithm with guaranteed convergence on global minima. A model for constructing cooperative PSO algorithms is developed, resulting in the introduction of two new PSO-based algorithms. Empirical results are presented to support the theoretical properties predicted by the various models, using synthetic benchmark functions to investigate specific properties. The various PSO-based algorithms are then applied to the task of training neural networks, corroborating the results obtained on the synthetic benchmark functions. The thesis investigates the behavior of the PSO algorithm, including formal proofs of convergence for the various new PSO-based algorithms introduced. Several cooperative PSO algorithms, based on the models discussed, are introduced. The convergence properties of these cooperative algorithms are investigated, with formal proofs where applicable. An empirical analysis of the behavior of the various PSO-based algorithms is presented, applied to minimisation tasks involving synthetic benchmark functions. These synthetic functions allow specific aspects of PSO behavior to be tested. The same PSO-based algorithms are used to train summation and product unit networks. These results are presented to show that the new algorithms introduced in this thesis have similar performance on both real-world and synthetic minimisation tasks. The thesis concludes with a summary of the findings and some topics for future research. Appendices present a glossary of terms, a definition of frequently used symbols, a derivation of the closed-form PSO equations, a set of 3D-plots of the synthetic benchmark functions used, a description of the gradient-based algorithms used, and a list of publications derived from the work presented.An Analysis of Particle Swarm Optimizers by Frans van den Bergh This thesis presents a theoretical model to describe the long-term behavior of the Particle Swarm Optimizer (PSO) algorithm. An enhanced version of the PSO is constructed and shown to have guaranteed convergence on local minima. This algorithm is extended further, resulting in an algorithm with guaranteed convergence on global minima. A model for constructing cooperative PSO algorithms is developed, resulting in the introduction of two new PSO-based algorithms. Empirical results are presented to support the theoretical properties predicted by the various models, using synthetic benchmark functions to investigate specific properties. The various PSO-based algorithms are then applied to the task of training neural networks, corroborating the results obtained on the synthetic benchmark functions. The thesis investigates the behavior of the PSO algorithm, including formal proofs of convergence for the various new PSO-based algorithms introduced. Several cooperative PSO algorithms, based on the models discussed, are introduced. The convergence properties of these cooperative algorithms are investigated, with formal proofs where applicable. An empirical analysis of the behavior of the various PSO-based algorithms is presented, applied to minimisation tasks involving synthetic benchmark functions. These synthetic functions allow specific aspects of PSO behavior to be tested. The same PSO-based algorithms are used to train summation and product unit networks. These results are presented to show that the new algorithms introduced in this thesis have similar performance on both real-world and synthetic minimisation tasks. The thesis concludes with a summary of the findings and some topics for future research. Appendices present a glossary of terms, a definition of frequently used symbols, a derivation of the closed-form PSO equations, a set of 3D-plots of the synthetic benchmark functions used, a description of the gradient-based algorithms used, and a list of publications derived from the work presented.