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Particle swarm optimization

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A particle swarm searching for the global minimum of a function

Particle swarm optimization (PSO) is a kind of computer method that helps find good answers to tricky problems. It works by copying how animals like birds and fish move in groups.[1] The idea was first shared in 1995 by James Kennedy, who studied how people behave, and Russell Eberhart, who worked in electrical engineering.[2] In PSO, a group of “particles” move around inside a “search space,” which is just the collection of all possible answers to the problem. Each particle is like a guess for the answer, and its position represents the details of that guess. As the particles “fly” through the space, they change their positions by looking at how good their own guesses are and how good the guesses of their neighbors are. Even though no single particle knows the whole answer, together they get closer and closer to the best one.[3]

The main idea comes from how animals in nature learn from each other. Each particle remembers the best guess it has ever made (this is called its “personal best”), and it also learns from the best guess that any particle in the whole group has made (this is called the “global best”). By moving toward these two points, the particles search many different places but also focus on areas that seem promising. How the particles move is controlled by settings such as “inertia weight,” which makes them keep going in the same direction for a while, and “acceleration coefficients,” which decide how strongly they are pulled toward their personal best or the group’s best.[4][5]

PSO can be used for many kinds of problems, especially when there are too many possible answers to check one by one. Engineers have used it to design airplane wings that are more efficient,[6] power companies have used it to plan the cheapest way to meet electricity demand,[7] and robot designers have used it to help robots move without crashing into things.[8] Scientists have also used it to train artificial brains called neural networks,[9] arrange antennas for better signals,[10] improve picture quality in image processing,[11] and study how pollution spreads in underground water.[12] Sometimes, PSO is combined with other problem-solving methods to make it even better.[13]

One reason PSO is popular is that it is simple to understand and does not take much code to write.[14] It can also adjust to changes while it is running, which makes it good for problems that change over time, like controlling traffic in real time.[15] Since particles share what they have learned through the group’s best answers, PSO can run on many computers at once to get results faster.[16] However, it does have weaknesses, if the particles all focus too quickly on one answer, they might miss better ones, and the method works best when its settings are chosen carefully. Even with these limits, PSO is still one of the most popular swarm-based methods for solving problems, showing how simple group behavior can lead to powerful teamwork in computers.[17]

References

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  1. ↑ Kennedy, J.; Eberhart, R. (1995). "Particle swarm optimization". Proceedings of ICNN'95 - International Conference on Neural Networks. 4: 1942–1948 vol.4. doi:10.1109/ICNN.1995.488968.
  2. ↑ Eberhart, R.; Kennedy, J. (1995). "A new optimizer using particle swarm theory". MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science: 39–43. doi:10.1109/MHS.1995.494215.
  3. ↑ Shi, Y.; Eberhart, R. (1998). "A modified particle swarm optimizer". 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360): 69–73. doi:10.1109/ICEC.1998.699146.
  4. ↑ Kennedy, James (2006), Zomaya, Albert Y. (ed.), "Swarm Intelligence", Handbook of Nature-Inspired and Innovative Computing: Integrating Classical Models with Emerging Technologies, Boston, MA: Springer US, pp. 187–219, doi:10.1007/0-387-27705-6_6, ISBN 978-0-387-27705-9, retrieved 2025-08-16
  5. ↑ Clerc, M.; Kennedy, J. (2002). "The particle swarm - explosion, stability, and convergence in a multidimensional complex space". IEEE Transactions on Evolutionary Computation. 6 (1): 58–73. doi:10.1109/4235.985692. ISSN 1941-0026.
  6. ↑ Skinner, S.N.; Zare-Behtash, H. (2018). "State-of-the-art in aerodynamic shape optimisation methods". Applied Soft Computing. 62: 933–962. doi:10.1016/j.asoc.2017.09.030.
  7. ↑ Gaing, Zwe-Lee (2003). "Particle swarm optimization to solving the economic dispatch considering the generator constraints". IEEE Transactions on Power Systems. 18 (3): 1187–1195. doi:10.1109/TPWRS.2003.814889. ISSN 1558-0679.
  8. ↑ Han-ye, Zhang,; Wei-ming, Lin,; Ai-xia, Chen, (2018). "Path Planning for the Mobile Robot: A Review". Symmetry. 10 (10). doi:10.3390/sym10100450. ISSN 2073-8994.{{cite journal}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link) CS1 maint: unflagged free DOI (link)
  9. ↑ Eberhart, Russell C.; Shi, Yuhui (1998). Porto, V. W.; Saravanan, N.; Waagen, D.; Eiben, A. E. (eds.). "Comparison between genetic algorithms and particle swarm optimization". Evolutionary Programming VII. Berlin, Heidelberg: Springer: 611–616. doi:10.1007/BFb0040812. ISBN 978-3-540-68515-9.
  10. ↑ Robinson, J.; Rahmat-Samii, Y. (2004). "Particle swarm optimization in electromagnetics". IEEE Transactions on Antennas and Propagation. 52 (2): 397–407. doi:10.1109/TAP.2004.823969. ISSN 1558-2221.
  11. ↑ Rodriguez-Sánchez, Rosa; García, J. A.; Fdez-Valdivia, J. (2011-10-15). "From computational attention to image fusion". Pattern Recognition Letters. 32 (14): 1778–1795. doi:10.1016/j.patrec.2011.07.003. ISSN 0167-8655.
  12. ↑ Severino, Gerardo; Santini, Alessandro (2005-09-01). "On the effective hydraulic conductivity in mean vertical unsaturated steady flows". Advances in Water Resources. 28 (9): 964–974. doi:10.1016/j.advwatres.2005.03.003. ISSN 0309-1708.
  13. ↑ Reisi-Nafchi, Mohammad; Moslehi, Ghasem (2015-08-01). "A hybrid genetic and linear programming algorithm for two-agent order acceptance and scheduling problem". Applied Soft Computing. 33: 37–47. doi:10.1016/j.asoc.2015.04.027. ISSN 1568-4946.
  14. ↑ Poli, Riccardo; Kennedy, James; Blackwell, Tim (2007-06-01). "Particle swarm optimization". Swarm Intelligence. 1 (1): 33–57. doi:10.1007/s11721-007-0002-0. ISSN 1935-3820.
  15. ↑ Celtek, Seyit Alperen; Durdu, Akif; Alı, Muzamil Eltejani Mohammed (2020-12-15). "Real-time traffic signal control with swarm optimization methods". Measurement. 166: 108206. doi:10.1016/j.measurement.2020.108206. ISSN 0263-2241.
  16. ↑ Charilogis, Vasileios; Tsoulos, Ioannis G.; Tzallas, Alexandros (2023-10-04). "An Improved Parallel Particle Swarm Optimization". SN Computer Science. 4 (6): 766. doi:10.1007/s42979-023-02227-9. ISSN 2661-8907.
  17. ↑ Clerc, Maurice (2006). Particle Swarm Optimization. Wiley. doi:10.1002/9780470612163. ISBN 978-1-905209-04-0.
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