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A Convergence Proof for the Particle Swarm Optimiser

Bergh F. van den, Engelbrecht A.P.

Fundamenta Informaticae

2011

Vol. 105, nr 4

341-374

The Particle Swarm Optimiser (PSO) is a population based stochastic optimisation algorithm, empirically shown to be efficient and robust. This paper provides a proof to show that the original PSO does not have guaranteed convergence to a local optimum. A flaw in the original PSO is identified which causes stagnation of the swarm. Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum. Further extensions with provable global convergence are also described. Experimental results are provided to elucidate the behavior of the modified PSO as well as PSO variations with global convergence.

Boosting Classifiers Built from Different Subsets of Features

Janodet J-C., Sebban M., Suchier H-M.

Fundamenta Informaticae

2009

Vol. 96, nr 1/2

89-109

We focus on the adaptation of boosting to representation spaces composed of different subsets of features. Rather than imposing a single weak learner to handle data that could come from different sources (e.g., images and texts and sounds), we suggest the decomposition of the learning task into several dependent sub-problems of boosting, treated by different weak learners, that will optimally collaborate during the weight update stage. To achieve this task, we introduce a new weighting scheme for which we provide theoretical results. Experiments are carried out and show that ourmethod works significantly better than any combination of independent boosting procedures.

Particle Swarms for Linearly Constrained Optimisation

Paquet U., Engelbrecht A.P.

Fundamenta Informaticae

2007

Vol. 76, nr 1-2

147-170

Particle Swarm Optimisation (PSO) has proved to be a very useful algorithm to optimise unconstrained functions. This paper extends PSO to a Linear PSO (LPSO) to optimise functions constrained by a set of equality constraints of the form Ax = b. By initialising particles within a constrained hyperplane, the LPSO is guaranteed to `fly' only through this hyperplane. A criterion on the initial swarm stipulates when the optimum solution can possibly be reached. The Linear PSO is modified to the Converging Linear PSO, for which it is proved to always find at least a local minimum. Experimental results are given, which compare the LPSO and CLPSO with Genocop II.