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m The description of the PSO problem above is cast as a minimization problem, yet, the algorithm solves a maximization problem. I hope my edits provide consistency. |
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The topology of the swarm defines the subset of particles with which each particle can exchange information.<ref name=kennedy2002population/> The basic version of the algorithm uses the global topology as the swarm communication structure.<ref name=bratton2007/> This topology allows all particles to communicate with all the other particles, thus the whole swarm share the same best position '''g''' from a single particle. However, this approach might lead the swarm to be trapped into a local minimum,<ref>Mendes, R. (2004). [https://pdfs.semanticscholar.org/d224/80b09d1f0759fb20e0fb0bd2de205457c8bc.pdf Population Topologies and Their Influence in Particle Swarm Performance] (PhD thesis). Universidade do Minho.</ref> thus different topologies have been used to control the flow of information among particles. For instance, in local topologies, particles only share information with a subset of particles.<ref name=bratton2007/> This subset can be a geometrical one<ref>Suganthan, Ponnuthurai N. "[https://ieeexplore.ieee.org/abstract/document/785514/ Particle swarm optimiser with neighbourhood operator]." Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on. Vol. 3. IEEE, 1999.</ref> – for example "the ''m'' nearest particles" – or, more often, a social one, i.e. a set of particles that is not depending on any distance. In such cases, the PSO variant is said to be local best (vs global best for the basic PSO).
A commonly used swarm topology is the ring, in which each particle has just two neighbours, but there are many others.<ref name=bratton2007/> The topology is not necessarily static. In fact, since the topology is related to the diversity of communication of the particles,<ref name=oliveira2016communication/> some efforts have been done to create adaptive topologies (SPSO,<ref>SPSO [http://www.particleswarm.info Particle Swarm Central]</ref> APSO,<ref> Almasi, O. N. and Khooban, M. H. (2017). A parsimonious SVM model selection criterion for classification of real-world data sets via an adaptive population-based algorithm. Neural Computing and Applications, 1-9. [https://link.springer.com/article/10.1007/s00521-017-2930-y https://doi.org/10.1007/s00521-017-2930-y]</ref> stochastic star,<ref>Miranda, V., Keko, H. and Duque, Á. J. (2008). [https://repositorio.inesctec.pt/bitstream/123456789/1561/1/PS-05818.pdf Stochastic Star Communication Topology in Evolutionary Particle Swarms (EPSO)]. International Journal of Computational Intelligence Research (IJCIR), Volume 4, Number 2, pp. 105-116</ref> TRIBES,<ref>Clerc, M. (2006). Particle Swarm Optimization. ISTE (International Scientific and Technical Encyclopedia), 2006</ref> Cyber Swarm,<ref>Yin, P., Glover, F., Laguna, M., & Zhu, J. (2011). [http://leeds-faculty.colorado.edu/glover/fred%20pubs/428%20-%20A_complementary_cyber_swarm_algorithm_pub%20version%20w%20pen%20et%20al.pdf A Complementary Cyber Swarm Algorithm]. International Journal of Swarm Intelligence Research (IJSIR), 2(2), 22-41</ref> and C-PSO<ref name=elshamy07sis/>)
== Inner workings ==
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