Swarm Intelligence

, Volume 1, Issue 1, pp 33–57 | Cite as

Particle swarm optimization

An overview
Article

Abstract

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.

Keywords

Particle swarms Particle swarm optimization PSO Social networks Swarm theory Swarm dynamics Real world applications 

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References

  1. Agrafiotis, D. K., & Cedeño, W. (2002). Feature selection for structure-activity correlation using binary particle swarms. Journal of Medicinal Chemistry, 45(5), 1098–1107. CrossRefGoogle Scholar
  2. Angeline, P. (1998). Evolutionary optimization versus particle swarm optimization: Philosophy and performance differences. In V. W. Porto, N. Saravanan, D. Waagen, & A. E. Eiben (Eds.), Proceedings of evolutionary programming VII (pp. 601–610). Berlin: Springer. CrossRefGoogle Scholar
  3. Bavelas, A. (1950). Communication patterns in task-oriented groups. Journal of the Acoustical Society of America, 22, 271–282. CrossRefGoogle Scholar
  4. Blackwell, T. M. (2003a). Particle swarms and population diversity I: Analysis. In A. M. Barry (Ed.), Proceedings of the bird of a feather workshops of the genetic and evolutionary computation conference (GECCO) (pp. 103–107), Chicago. San Francisco: Kaufmann. Google Scholar
  5. Blackwell, T. M. (2003b). Particle swarms and population diversity II: Experiments. In A. M. Barry (Ed.), Proceedings of the bird of a feather workshops of the genetic and evolutionary computation conference (GECCO) (pp. 108–112), Chicago. San Francisco: Kaufmann. Google Scholar
  6. Blackwell, T. M. (2005). Particle swarms and population diversity. Soft Computing, 9, 793–802. MATHCrossRefGoogle Scholar
  7. Blackwell, T. M. (2007). Particle swarm optimization in dynamic environments. In S. Yand, Y. Ong, & Y. Jin (Eds.), Evolutionary computation in dynamic environments (pp. 29–49). Springer, Berlin. DOI 10.1007/978-3-540-49774-5-2.
  8. Blackwell, T., & Bentley, P. J. (2002). Don’t push me! Collision-avoiding swarms. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1691–1696), Honolulu, HI. Piscataway: IEEE. Google Scholar
  9. Blackwell, T. M., & Branke, J. (2006). Multi-swarms, exclusion and anti-convergence on dynamic environments. IEEE Transactions on Evolutionary Computation, 10, 459–472. CrossRefGoogle Scholar
  10. Brandstatter, B., & Baumgartner, U. (2002). Particle swarm optimization-mass-spring system analogon. IEEE Transactions on Magnetics, 38(2), 997–1000. CrossRefGoogle Scholar
  11. Campana, E. F., Fasano, G., & Pinto, A. (2006a). Dynamic system analysis and initial particles position in particle swarm optimization. In Proceedings of the IEEE swarm intelligence symposium (SIS), Indianapolis. Piscataway: IEEE. Google Scholar
  12. Campana, E. F., Fasano, G., Peri, D., & Pinto, A. (2006b). Particle swarm optimization: Efficient globally convergent modifications. In C. A. Mota Soares, et al. (Eds.), Proceedings of the III European conference on computational mechanics, solids, structures and coupled problems in engineering, Lisbon, Portugal. Google Scholar
  13. Carlisle, A., & Dozier, G. (2000). Adapting particle swarm optimization to dynamic environments. In Proceedings of international conference on artificial intelligence (pp. 429–434), Las Vegas, NE. Google Scholar
  14. Carlisle, A., & Dozier, G. (2001). Tracking changing extrema with particle swarm optimizer. Auburn University Technical Report CSSE01-08. Google Scholar
  15. Clerc, M. (2004). Discrete particle swarm optimization, illustrated by the traveling salesman problem. In B. V. Babu & G. C. Onwubolu (Eds.), New optimization techniques in engineering (pp. 219–239). Berlin: Springer. Google Scholar
  16. Clerc, M. (2006a). Stagnation analysis in particle swarm optimization or what happens when nothing happens. Technical Report CSM-460, Department of Computer Science, University of Essex, August 2006. Google Scholar
  17. Clerc, M. (2006b). Particle swarm optimization. London: ISTE. MATHGoogle Scholar
  18. Clerc, M., & Kennedy, J. (2002). The particle swarm—explosion, stability, and convergence in a multidimensional complex space. IEEE Transaction on Evolutionary Computation, 6(1), 58–73. CrossRefGoogle Scholar
  19. Dorigo, M., & Stützle, T. (2004). Ant colony optimization. Cambridge: MIT Press. MATHGoogle Scholar
  20. Eberhart, R. C., & Kennedy, J. (1995). A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science (pp. 39–43), Nagoya, Japan. Piscataway: IEEE. CrossRefGoogle Scholar
  21. Eberhart, R. C., & Shi, Y. (2000). Comparing inertia weights and constriction factors in particle swarm optimization. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 84–88), San Diego, CA. Piscataway: IEEE. Google Scholar
  22. Eberhart, R. C., & Shi, Y. (2001). Tracking and optimizing dynamic systems with particle swarms. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 94–100), Seoul, Korea. Piscataway: IEEE. Google Scholar
  23. Eberhart, R. C., Simpson, P. K., & Dobbins, R. W. (1996). Computational intelligence PC tools. Boston: Academic Press. Google Scholar
  24. Engelbrecht, A. P. (2005). Fundamentals of computational swarm intelligence. Chichester: Wiley. Google Scholar
  25. Hendtlass, T. (2001). A combined swarm differential evolution algorithm for optimization problems. In L. Monostori, J. Váncza & M. Ali (Eds.), Lecture notes in computer science : Vol. 2070. Proceedings of the 14th international conference on industrial and engineering applications of artificial intelligence and expert systems (IEA/AIE) (pp. 11–18), Budapest, Hungary. Berlin: Springer. Google Scholar
  26. Heppner, H., & Grenander, U. (1990). A stochastic non-linear model for coordinated bird flocks. In S. Krasner (Ed.), The ubiquity of chaos (pp. 233–238). Washington: AAAS. Google Scholar
  27. Holden, N., & Freitas, A. A. (2005). A hybrid particle swarm/ant colony algorithm for the classification of hierarchical biological data. In Proceedings of the IEEE swarm intelligence symposium (SIS) (pp. 100–107). Piscataway: IEEE. CrossRefGoogle Scholar
  28. Hu, X., & Eberhart, R. C. (2001). Tracking dynamic systems with PSO: where’s the cheese? In Proceedings of the workshop on particle swarm optimization. Purdue school of engineering and technology, Indianapolis, IN. Google Scholar
  29. Hu, X., & Eberhart, R. C. (2002). Adaptive particle swarm optimization: detection and response to dynamic systems. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1666–1670), Honolulu, HI. Piscataway: IEEE. Google Scholar
  30. Iqbal, M., & Montes de Oca, M. A. (2006). An estimation of distribution particle swarm optimization algorithm. In M. Dorigo, L. M. Gambardella, M. Birattari, A. Martinoli, R. Poli & T. Stützle (Eds.), Lecture notes in computer science : Vol. 4150. Proceedings of the fifth international workshop on ant colony optimization and swarm intelligence ANTS 2006 (pp. 72–83). Berlin: Springer. CrossRefGoogle Scholar
  31. Iwasaki, N., & Yasuda, K. (2005). Adaptive particle swarm optimization using velocity feedback. International Journal of Innovative Computing, Information and Control, 1(3), 369–380. Google Scholar
  32. Janson, S., & Middendorf, M. (2004). A hierarchical particle swarm optimizer for dynamic optimization problems. In G. R. Raidl (Ed.), Lecture notes in computer science : Vol. 3005. Proceedings of evoworkshops 2004: 1st European workshop on evolutionary algorithms in stochastic and dynamic environments (pp. 513–524), Coimbra, Portugal. Berlin: Springer. Google Scholar
  33. Janson, S., & Middendorf, M. (2005). A hierarchical particle swarm optimizer and its adaptive variant. IEEE Transactions on System Man and Cybernetics B, 35(6), 1272–1282. CrossRefGoogle Scholar
  34. Kadirkamanathan, V., Selvarajah, K., & Fleming, P. J. (2006). Stability analysis of the particle dynamics in particle swarm optimizer. IEEE Transactions on Evolutionary Computation, 10(3), 245–255. CrossRefGoogle Scholar
  35. Kennedy, J. (1998). The behavior of particles. In V. W. Porto, N. Saravanan, D. Waagen & A. E. Eiben (Eds.), Lecture notes in computer science. Evolutionary programming VII: proceedings of the 7-th annual conference on evolutionary programming (pp. 581–589). San Diego, CA. Berlin: Springer. Google Scholar
  36. Kennedy, J. (1999). Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In Proceedings of the IEEE congress on evolutionary computation (pp. 1931–1938). Piscataway: IEEE. Google Scholar
  37. Kennedy, J. (2003). Bare bones particle swarms. In Proceedings of the IEEE swarm intelligence symposium (SIS) (pp. 80–87), Indianapolis, IN. Piscataway: IEEE. CrossRefGoogle Scholar
  38. Kennedy, J. (2004). Probability and dynamics in the particle swarm. In IEEE congress on evolutionary computation (CEC04) (pp. 340–347). Piscataway: IEEE. Google Scholar
  39. Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. In Proceedings of the IEEE international conference on neural networks IV (pp. 1942–1948). Piscataway: IEEE. CrossRefGoogle Scholar
  40. Kennedy, J., & Eberhart, R. C. (1997). A discrete binary version of the particle swarm algorithm. In Proceedings of the conference on systems, man, and cybernetics (pp. 4104–4109). Piscataway: IEEE. Google Scholar
  41. Kennedy, J., & Mendes, R. (2002). Population structure and particle swarm performance. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1671–1676), Honolulu, HI. Piscataway: IEEE. Google Scholar
  42. Kennedy, J., & Spears, W. M. (1998). Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator. In Proceedings international conference on evolutionary computation (pp. 78–83). Piscataway: IEEE. CrossRefGoogle Scholar
  43. Kennedy, J., Eberhart, R. C., & Shi, Y. (2001). Swarm intelligence. San Francisco: Kaufmann. Google Scholar
  44. Krink, T., & Loøvbjerg, M. (2002). The LifeCycle model: combining particle swarm optimization, genetic algorithms and hillclimbers. In Lecture notes in computer science. Proceedings of parallel problem solving from nature (PPSN) (pp. 621–630). Granada, Spain. Berlin: Springer. Google Scholar
  45. Krink, T., Vesterstroøm, J. S., & Riget, J. (2002). Particle swarm optimization with spatial particle extension. In Proceedings of the IEEE congress on evolutionary computation (CEC-2002) (pp. 1474–1479). Piscataway: IEEE. Google Scholar
  46. Langdon, W. B., & Poli, R. (2005). Evolving problems to learn about particle swarm and other optimisers. In D. Corne et al. (Eds.), Proceedings of IEEE congress on evolutionary computation (CEC) (pp. 81–88), Edinburgh, UK. Piscataway: IEEE. CrossRefGoogle Scholar
  47. Langdon, W. B., & Poli, R. (2006). Finding social landscapes for PSOs via kernels. In G. G. Yen, L. Wang, P. Bonissone, & S. M. Lucas (Eds.), Proceedings of the 2006 IEEE congress on evolutionary computation (CEC) (pp. 6118–6125), Vancouver, Canada. Piscataway: IEEE. Google Scholar
  48. Langdon, W. B., & Poli, R. (2007, accepted for publication). Evolving problems to learn about particle swarm optimisers and other search algorithms. IEEE Transaction on Evolutionary Computation. DOI 10.1109/TEVC.2006.886448.
  49. Langdon, W. B., Poli, R., Holland, O., & Krink, T. (2005). Understanding particle swarm optimization by evolving problem landscapes. In L. M. Gambardella, P. Arabshahi & A. Martinoli (Eds.), Proceedings SIS 2005 IEEE swarm intelligence (pp. 30–37), Pasadena, CA. Piscataway: IEEE. CrossRefGoogle Scholar
  50. Li, X., & Dam, K. H. (2003). Comparing particle swarms for tracking extrema in dynamic environments. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1772–1779). Piscataway: IEEE. Google Scholar
  51. Liang, J. J., & Suganthan, P. N. (2005). Dynamic multiswarm particle swarm optimizer (DMS-PSO). In Proceedings of the IEEE swarm intelligence symposium (SIS) (pp. 124–129). Piscataway: IEEE. CrossRefGoogle Scholar
  52. Loøvbjerg, M., & Krink, T. (2002). Extending particle swarms with self-organized criticality. In Proceedings of the IEEE congress on evolutionary computation (CEC-2002) (pp. 1588–1593). Piscataway: IEEE. Google Scholar
  53. Loøvbjerg, M., Rasmussen, T. K., & Krink, T. (2001). Hybrid particle swarm optimiser with breeding and subpopulations. In Proceedings of the third genetic and evolutionary computation conference (GECCO) (pp. 469–476). San Francisco: Kaufmann. Google Scholar
  54. Mendes, R. (2004). Population topologies and their influence in particle swarm performance. PhD thesis, Departamento de Informatica, Escola de Engenharia, Universidade do Minho, 2004. Google Scholar
  55. Mendes, R., Cortes, P., Rocha, M., & Neves, J. (2002). Particle swarms for feedforward neural net training. In Proceedings of the international joint conference on neural networks (pp. 1895–1899), Honolulu, HI. Piscataway: IEEE. Google Scholar
  56. Mendes, R., Kennedy, J., & Neves, J. (2003). Watch thy neighbor or how the swarm can learn from its environment. In Proceedings of the IEEE swarm intelligence symposium (SIS) (pp. 88–94). Piscataway: IEEE. CrossRefGoogle Scholar
  57. Miranda, V., & Fonseca, N. (2002). New evolutionary particle swarm algorithm (EPSO) applied to voltage/VAR control. In Proceedings of the 14th power systems computation conference (PSCC) (Session 21, Paper 5, pp. 1–6), Seville, Spain. Google Scholar
  58. Mohan, C. K., & Al-Kazemi, B. (2001). Discrete particle swarm optimization. In Proceedings of the workshop on particle swarm optimization, Indianapolis, IN, Purdue School of Engineering and Technology, IUPUI. Google Scholar
  59. Moraglio, A., Di Chio, C., & Poli, R. (2007). Geometric particle swarm optimization. In M. Ebner et al. (Eds.), Lecture notes in computer science : Vol. 4445. Proceedings of the European conference on genetic programming (EuroGP). (pp. 125–136). Berlin: Springer. Google Scholar
  60. Ozcan, E., & Mohan, C. K. (1998). Analysis of a simple particle swarm optimization system. Intelligent Engineering Systems Through Artificial Neural Networks, 8, 253–258. Google Scholar
  61. Ozcan, E., & Mohan, C. (1999). Particle swarm optimization: surfing the waves. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1939–1944). Piscataway: IEEE. Google Scholar
  62. Pamparä, G., Franken, N., & Engelbrecht, A. P. (2005). Combining particle swarm optimization with angle modulation to solve binary problems. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 225–239). Piscataway: IEEE. Google Scholar
  63. Parrot, D., & Li, X. (2006). Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Transactions on Evolutionary Computation, 10, 440–458. CrossRefGoogle Scholar
  64. Parsopoulos, K. E., & Vrahatis, M. N. (2001). Particle swarm optimizer in noisy and continuously changing environments. In M. H. Hamza (Ed.), Artificial intelligence and soft computing (pp. 289–294). Anaheim: IASTED/ACTA. Google Scholar
  65. Parsopoulos, K. E., & Vrahatis, M. N. (2004). On the computation of all global minimizers through particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8, 211–224. CrossRefGoogle Scholar
  66. Peram, T., Veeramachaneni, K., & Mohan, C. (2003). Fitness-distance ratio based particle swarm optimization. In Proceedings of the IEEE swarm intelligence symposium (SIS) (pp. 174–181), Indianapolis, IN. Piscataway: IEEE. CrossRefGoogle Scholar
  67. Poli, R. (2007a). An analysis of publications on particle swarm optimization applications. Technical Report CSM-469, Department of Computer Science, University of Essex. Google Scholar
  68. Poli, R. (2007b, forthcoming). On the moments of the sampling distribution of particle swarm optimisers. In Proceedings of the workshop on particle swarm optimization: the second decade of the genetic and evolutionary computation conference (GECCO), London, July 2007. New York: ACM. Google Scholar
  69. Poli, R., & Broomhead, D. (2007, forthcoming). Exact analysis of the sampling distribution for the canonical particle swarm optimiser and its convergence during stagnation. In Genetic and evolutionary computation conference (GECCO), London. ACM, New York. Google Scholar
  70. Poli, R., & Stephens, C. R. (2004). Constrained molecular dynamics as a search and optimization tool. In M. Keijzer et al. (Eds.), Lecture notes in computer science : Vol. 3003. Proceedings of the 7th European conference on genetic programming (EuroGP) (pp. 150–161), Coimbra, Portugal. Berlin: Springer. Google Scholar
  71. Poli, R., Di Chio, C., & Langdon, W. B. (2005a). Exploring extended particle swarms: a genetic programming approach. In H.-G. Beyer, et al. (Eds.), GECCO 2005: Proceedings of the 2005 conference on genetic and evolutionary computation (pp. 169–176), Washington, DC. New York: ACM. CrossRefGoogle Scholar
  72. Poli, R., Langdon, W. B., & Holland, O. (2005b). Extending particle swarm optimization via genetic programming. In M. Keijzer et al. (Eds.), Lecture notes in computer science : Vol. 3447. Proceedings of the 8th European conference on genetic programming (pp. 291–300), Lausanne, Switzerland. Berlin: Springer. Google Scholar
  73. Poli, R., Langdon, W. B., Marrow, P., Kennedy, J., Clerc, M., Bratton, D., & Holden, N. (2006a). Communication, leadership, publicity and group formation in particle swarms. In Lecture notes in computer science : Vol. 4150. International workshop on Ant colony optimization and swarm intelligence (ANTS) (pp. 132–143). Berlin: Springer. CrossRefGoogle Scholar
  74. Poli, R., Wright, A. H., McPhee, N. F., & Langdon, W. B. (2006b). Emergent behaviour, population-based search and low-pass filtering. In Proceedings of the IEEE world congress on computational intelligence, IEEE congress on evolutionary computation (CEC) (pp. 395–402), Vancouver. Piscataway: IEEE. Google Scholar
  75. Poli, R., Langdon, W. B., Clerc, M., & Stephens, C. R. (2007, forthcoming). Continuous optimization theory made easy? Finite-element models of evolutionary strategies, genetic algorithms and particle swarm optimizers. In Lecture notes in computer science. Proceedings of the foundations of genetic algorithms (FOGA) workshop. Springer, Berlin, Germany. (Also available as Technical Report CSM-463, Department of Computer Science, University of Essex.) Google Scholar
  76. Pugh, J., Martinoli, A., & Zhang, Y. (2005). Particle swarm optimization for unsupervised robotic learning. In Proceedings of IEEE swarm intelligence symposium (SIS) (pp. 92–99). Piscataway: IEEE. CrossRefGoogle Scholar
  77. Reynolds, C. W. (1987). Flocks, herds, and schools: a distributed behavioral model. Computer Graphics, 21(4), 25–34. CrossRefMathSciNetGoogle Scholar
  78. Richer., T., & Blackwell, T. M. (2006). The Lévy particle swarm. In Proceedings of IEEE congress on evolutionary computation (pp. 3150–3157), Vancouver. Piscataway: IEEE. Google Scholar
  79. Robinson, J., Sinton, S., & Rahmat-Samii, Y. (2002). Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. In Proceedings IEEE international symposium on antennas and propagation (pp. 314–317), San Antonio, TX. Piscataway: IEEE. Google Scholar
  80. Rudolph, G. (1996). Convergence of evolutionary algorithms in general search spaces. In Proceedings of the IEEE international conference on evolutionary computation (pp. 50–54), Nayoya University, Japan. Piscataway: IEEE. CrossRefGoogle Scholar
  81. Secrest, B., & Lamont, G. (2003). Visualizing particle swarm optimization—Gaussian particle swarm optimization. In Proceedings of the IEEE swarm intelligence symposium (SIS) (pp. 198–204). Piscataway: IEEE. CrossRefGoogle Scholar
  82. Shi, Y., & Eberhart, R. C. (1998b). A modified particle swarm optimizer. In Proceedings of the IEEE international conference on evolutionary computation (pp. 69–73). Piscataway: IEEE. CrossRefGoogle Scholar
  83. Suganthan, P. N. (1999). Particle swarm optimiser with neighbourhood operator. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1958–1962). Piscataway: IEEE. Google Scholar
  84. Trelea, I. C. (2003). The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters, 85(6), 317–325. CrossRefMathSciNetGoogle Scholar
  85. van den Bergh, F. (2002). An analysis of particle swarm optimizers. PhD thesis, Department of Computer Science, University of Pretoria, Pretoria, South Africa. Google Scholar
  86. Vesterstroøm, J. S., Riget, J., & Krink, T. (2002). Division of labor in particle swarm optimization. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1570–1575), Honolulu, HI. Piscataway: IEEE. Google Scholar
  87. Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442. CrossRefGoogle Scholar
  88. Wei, C., He, Z., Zhang, Y., & Pei, W. (2002). Swarm directions embedded in fast evolutionary programming. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1278–1283), Honolulu, HI. Piscataway: IEEE. Google Scholar
  89. Xie, X., Zhang, W., & Yang, Z. (2002). Dissipative particle swarm optimization. In Proceedings of the IEEE congress on evolutionary computation (CEC) (pp. 1456–1461), Honolulu, HI. Piscataway: IEEE. Google Scholar
  90. Yasuda, K., Ide, A., & Iwasaki, N. (2003). Adaptive particle swarm optimization. In Proceedings of the IEEE international conference on systems, man and cybernetics (pp. 1554–1559). Piscataway: IEEE. Google Scholar
  91. Zhang, W.-J., & Xie, X.-F. (2003). DEPSO: hybrid particle swarm with differential evolution operator. In Proceedings of the IEEE International conference on systems, man and cybernetics (SMCC) (pp. 3816–3821), Washington, DC. Piscataway: IEEE. Google Scholar
  92. Zheng, Y.-L., Ma, L.-H., Zhang, L.-Y., & Qian, J.-X. (2003). On the convergence analysis and parameter selection in particle swarm optimization. In Proceedings of the IEEE international conference on machine learning and cybernetics (pp. 1802–1807). Piscataway: IEEE. Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Computing and Electronic SystemsUniversity of EssexEssexUK
  2. 2.WashingtonUSA
  3. 3.Department of ComputingGoldsmiths CollegeLondonUK

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