Particle swarm optimization (PSO) has undergone many changes since its introduction in 1995. As researchers have learned about the technique, they have derived new versions, developed new applications, and published theoretical studies of the effects of the various parameters and aspects of the algorithm. This paper comprises a snapshot of particle swarming from the authors' perspective, including variations in the algorithm, current and ongoing research, applications and open problems.

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Particle swarm optimisation (PSO) has been enormously successful. Within little more than a decade hundreds of papers have reported successful applications of PSO. In fact, there are so many of them, that it is difficult for PSO practitioners and researchers to have a clear up-to-date vision of what has been done in the area of PSO applications. This brief paper attempts to fill this gap, by categorising a large number of publications dealing with PSO applications stored in the IEEE Xplore database at the time of writing.

We review the main results obtained in the theory of schemata in genetic programming (GP), emphasizing their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP, which is closer to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, one-point crossover, and point mutation, this concept of schema has been used to derive an improved schema theorem for GP that describes the propagation of schemata from one generation to the next. We discuss this result and show that our schema theorem is the natural counterpart for GP of the schema theorem for GAs, to which it asymptotically converges.

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