Flocks, herds and schools: A distributed behavioral model
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
The particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters
Information Processing Letters
Dynamics and stability of the sampling distribution of particle swarm optimisers via moment analysis
Journal of Artificial Evolution and Applications - Particle Swarms: The Second Decade
The generalized PSO: a new door to PSO evolution
Journal of Artificial Evolution and Applications - Particle Swarms: The Second Decade
A study of particle swarm optimization particle trajectories
Information Sciences: an International Journal
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
The fully informed particle swarm: simpler, maybe better
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Stochastic Stability Analysis of the Linear Continuous and Discrete PSO Models
IEEE Transactions on Evolutionary Computation
Accelerating Gaussian bare-bones differential evolution using neighbourhood mutation
International Journal of Computing Science and Mathematics
An improved diversity-guided particle swarm optimisation for numerical optimisation
International Journal of Computing Science and Mathematics
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Particle swarm optimisation PSO is an evolutionary algorithm that has been successfully applied to many optimisation problems in different fields. PSO has been heuristically proposed based in a social analogy for large groups in nature. Since its publication, research has been carried to understand the PSO convergence and improving its numerical performance. Accordingly several modifications of the basic PSO have been proposed, mostly in a heuristic way. Nevertheless, many of these modifications were not really needed, since they were proposed based on a deficient mathematical analysis of the PSO stability conditions. PSO trajectories are stochastic processes and PSO can be considered as a discrete stochastic gradient algorithm. Nevertheless, PSO is not heuristic, since its convergence and the stability of particle trajectories are related. In conclusion, it is time for uniformisation, because paradoxically this wide range of PSO versions have generated mistrust, providing the impression that PSO success depends more on the version that has been adopted and on the skills of the PSO designer.