Advertisement

Soft Computing

, Volume 22, Issue 2, pp 387–408 | Cite as

Particle swarm optimization algorithm: an overview

  • Dongshu Wang
  • Dapei Tan
  • Lei Liu
Foundations

Abstract

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. Since presented in 1995, it has experienced a multitude of enhancements. As researchers have learned about the technique, they derived new versions aiming to different demands, developed new applications in a host of areas, published theoretical studies of the effects of the various parameters and proposed many variants of the algorithm. This paper introduces its origin and background and carries out the theory analysis of the PSO. Then, we analyze its present situation of research and application in algorithm structure, parameter selection, topology structure, discrete PSO algorithm and parallel PSO algorithm, multi-objective optimization PSO and its engineering applications. Finally, the existing problems are analyzed and future research directions are presented.

Keywords

Particle swarm optimization Topology structure Discrete PSO Parallel PSO Multi-objective optimization PSO 

Notes

Acknowledgements

The authors thank the reviewers for their valuable comments/suggestions which helped to improve the quality of this paper significantly.

Compliance with ethical standards

Funding

This study was funded by National Natural Sciences Funds of China (Grant Number 61174085).

Conflict of interest

All the authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Supplementary material

500_2016_2474_MOESM1_ESM.pdf (97 kb)
Supplementary material 1 (pdf 97 KB)

References

  1. Abdelbar AM, Abdelshahid S, Wunsch DCI (2005) Fuzzy pso: a generalization of particle swarm optimization. In: Proceedings of 2005 IEEE international joint conference on neural networks (IJCNN ’05) Montreal, Canada, July 31–August 4, pp 1086–1091Google Scholar
  2. Acan A, Gunay A (2005) Enhanced particle swarm optimization through external memory support. In: Proceedings of 2005 IEEE congress on evolutionary computation, Edinburgh, UK, Sept 2–4, pp 1875–1882Google Scholar
  3. Afshinmanesh F, Marandi A, Rahimi-Kian A (2005) A novel binary particle swarm optimization method using artificial immune system. In: Proceedings of the international conference on computer as a tool (EUROCON 2005) Belgrade, Serbia, Nov 21–24, pp 217–220Google Scholar
  4. Al-kazemi B, Mohan CK (2002) Multi-phase generalization of the particle swarm optimization algorithm. In: Proceedings of 2002 IEEE Congress on Evolutionary Computation, Honolulu, Hawaii, August 7–9, pp 489–494Google Scholar
  5. al Rifaie MM, Blackwell T (2012) Bare bones particle swarms with jumps ants. Lect Notes Comput Sci Ser 7461(1):49–60CrossRefGoogle Scholar
  6. Angeline PJ (1998a) Evolutionary optimization versus particle swarm optimization philosophy and performance difference. In: Evolutionary programming, Lecture notes in computer science, vol. vii edition. Springer, BerlinGoogle Scholar
  7. Angeline PJ (1998b) Using selection to improve particle swarm optimization. In: Proceedings of the 1998 IEEE international conference on evolutionary computation, Anchorage, Alaska, USA, May 4–9, pp 84–89Google Scholar
  8. Ardizzon G, Cavazzini G, Pavesi G (2015) Adaptive acceleration coefficients for a new search diversification strategy in particle swarm optimization algorithms. Inf Sci 299:337–378CrossRefGoogle Scholar
  9. Banka H, Dara S (2015) A hamming distance based binary particle swarm optimization (HDBPSO) algorithm for high dimensional feature selection, classification and validation. Pattern Recognit Lett 52:94–100CrossRefGoogle Scholar
  10. Barisal AK (2013) Dynamic search space squeezing strategy based intelligent algorithm solutions to economic dispatch with multiple fuels. Electr Power Energy Syst 45:50–59CrossRefGoogle Scholar
  11. Bartz-Beielstein T, Parsopoulos KE, Vrahatis MN (2002) Tuning pso parameters through sensitivity analysis. Technical Report CI 124/02, SFB 531. University of Dortmund, Dortmund, Germany, Department of Computer ScienceGoogle Scholar
  12. Bartz-Beielstein T, Parsopoulos KE, Vegt MD, Vrahatis MN (2004a) Designing particle swarm optimization with regression trees. Technical Report CI 173/04, SFB 531. University of Dortmund, Dortmund, Germany, Department of Computer ScienceGoogle Scholar
  13. Bartz-Beielstein T, Parsopoulos KE, Vrahatis MN (2004b) Analysis of particle swarm optimization using computational statistics. In: Proceedings of the international conference of numerical analysis and applied mathematics (ICNAAM 2004), Chalkis, Greece, pp 34–37Google Scholar
  14. Beheshti Z, Shamsuddin SM (2015) Non-parametric particle swarm optimization for global optimization. Appl Soft Comput 28:345–359CrossRefGoogle Scholar
  15. Benameur L, Alami J, Imrani A (2006) Adaptively choosing niching parameters in a PSO. In: Proceedings of genetic and evolutionary computation conference (GECCO 2006), Seattle, Washington, USA, July 8–12, pp 3–9Google Scholar
  16. Binkley KJ, Hagiwara M (2005) Particle swarm optimization with area of influence: increasing the effectiveness of the swarm. In: Proceedings of 2005 IEEE swarm intelligence symposium (SIS 2005), Pasadena, California, USA, June 8–10, pp 45–52Google Scholar
  17. Blackwell TM (2005) Particle swarms and population diversity. Soft Comput 9(11):793–802MATHCrossRefGoogle Scholar
  18. Blackwell TM, Bentley PJ (2002) Don’t push me! Collision-avoiding swarms. In: Proceedings of IEEE congress on evolutionary computation, Honolulu, HI, USA, August 7–9, pp 1691–1697Google Scholar
  19. Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: Proceedings of the 2007 IEEE swarm intelligence symposium (SIS2007), Honolulu, HI, USA, April 19–23, pp 120–127Google Scholar
  20. Brits R, Engelbrecht AP, van den Bergh F (2002) Solving systems of unconstrained equations using particle swarm optimization. In: Proceedings of IEEE international conference on systems, man, and cybernetics, hammamet, Tunisia, October 6–9, 2002. July 27–28, 2013, East Lansing, Michigan, pp 1–9Google Scholar
  21. Brits R, Engelbrecht AP, van den Bergh F (2003) Scalability of niche PSO. In: Proceedings of the IEEE swarm intelligence symposium, Indianapolis, Indiana, USA, April 24–26, pp 228–234Google Scholar
  22. Carlisle A, Dozier G (2000) Adapting particle swarm optimization to dynamic environments. In: Proceedings of the international conference on artificial intelligence, Athens, GA, USA, July 31–August 5, pp 429–434Google Scholar
  23. Carlisle A, Dozier G (2001) An off-the-shelf PSO. In: Proceedings of the workshop on particle swarm optimization, Indianapolis, Indiana, USAGoogle Scholar
  24. Chang WD (2015) A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems. Appl Soft Comput 33:170–182CrossRefGoogle Scholar
  25. Chatterjee A, Siarry P (2006) Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Comput Oper Res 33:859–871MATHCrossRefGoogle Scholar
  26. Chaturvedi KT, Pandit M, Shrivastava L (2008) Self-organizing hierarchical particle swarm optimization for non-convex economic dispatch. IEEE Trans Power Syst 23(3):1079–1087CrossRefGoogle Scholar
  27. Chen J, Pan F, Cai T (2006a) Acceleration factor harmonious particle swarm optimizer. Int J Autom Comput 3(1):41–46CrossRefGoogle Scholar
  28. Chen K, Li T, Cao T (2006b) Tribe-PSO: a novel global optimization algorithm and its application in molecular docking. Chemom Intell Lab Syst 82:248–259CrossRefGoogle Scholar
  29. Chen W, Zhang J, Lin Y, Chen N, Zhan Z, Chung H, Li Y, Shi Y (2013) Particle swarm optimization with an aging leader and challenger. IEEE Trans Evolut Comput 17(2):241–258CrossRefGoogle Scholar
  30. Chen Y, Feng Y, Li X (2014) A parallel system for adaptive optics based on parallel mutation PSO algorithm. Optik 125:329–332CrossRefGoogle Scholar
  31. Ciuprina G, Ioan D, Munteanu I (2007) Use of intelligent-particle swarm optimization in electromagnetics. IEEE Trans Manag 38(2):1037–1040Google Scholar
  32. Clerc M (1999) The swarm and the queen: towards a deterministic and adaptive particle swarm optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC 1999), pp 1951–1957, Washington, DC, USA, July 6–9, 1999Google Scholar
  33. Clerc M (2004) Discrete particle swarm optimization. In: Onwubolu GC (ed) New optimization techniques in engineering. Springer, BerlinGoogle Scholar
  34. Clerc M (2006) Stagnation analysis in particle swarm optimisation or what happens when nothing happens. Technical Report CSM-460, Department of Computer Science, University of Essex, Essex, UK, August 5–8, 2006Google Scholar
  35. Clerc M, Kennedy J (2002) The particle swarm-explosion, stability and convergence in a multi dimensional complex space. IEEE Trans Evolut Comput 6(2):58–73CrossRefGoogle Scholar
  36. Coelho LDS, Lee CS (2008) Solving economic load dispatch problems in power systems using chaotic and gaussian particle swarm optimization approaches. Electr Power Energy Syst 30:297–307CrossRefGoogle Scholar
  37. Coello CAC, Pulido G, Lechuga M (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evolut Comput 8(3):256–279CrossRefGoogle Scholar
  38. Deb K, Pratap A (2002) A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE Trans Evolut Comput 6(2):182–197CrossRefGoogle Scholar
  39. del Valle Y, Venayagamoorthy GK, Mohagheghi S, Hernandez JC, Harley RG (2008) Particle swarm optimization: basic concepts, variants and applications in power systems. IEEE Trans Evolut Comput 12:171–195CrossRefGoogle Scholar
  40. Diosan L, Oltean M (2006) Evolving the structure of the particle swarm optimization algorithms. In: Proceedings of European conference on evolutionary computation in combinatorial optimization (EvoCOP2006), pp 25–36, Budapest, Hungary, April 10–12, 2006Google Scholar
  41. Doctor S, Venayagamoorthy GK (2005) Improving the performance of particle swarm optimization using adaptive critics designs. In: Proceedings of 2005 IEEE swarm intelligence symposium (SIS 2005), pp 393–396, Pasadena, California, USA, June 8–10, 2005Google Scholar
  42. Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, pp 39–43, Nagoya, Japan, Mar 13–16, 1995Google Scholar
  43. Eberhart RC, Shi Y (2000) Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2000), pp 84–88, San Diego, CA, USA, July 16–19, 2000Google Scholar
  44. Eberhart RC, Shi Y (2001) Particle swarm optimization: developments, applications and resources. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2001), pp 81–86, Seoul, Korea, May 27–30Google Scholar
  45. El-Wakeel AS (2014) Design optimization of pm couplings using hybrid particle swarm optimization-simplex method (PSO-SM) algorithm. Electr Power Syst Res 116:29–35CrossRefGoogle Scholar
  46. Emara HM, Fattah HAA (2004) Continuous swarm optimization technique with stability analysis. In: Proceedings of American Control Conference, pp 2811–2817, Boston, MA, USA, June 30–July 2, 2004Google Scholar
  47. Engelbrecht AP, Masiye BS, Pampard G (2005) Niching ability of basic particle swarm optimization algorithms. In: Proceedings of 2005 IEEE Swarm Intelligence Symposium (SIS 2005), pp 397–400, Pasadena, CA, USA, June 8–10, 2005Google Scholar
  48. Fan H (2002) A modification to particle swarm optimization algorithm. Eng Comput 19(8):970–989MATHCrossRefGoogle Scholar
  49. Fan Q, Yan X (2014) Self-adaptive particle swarm optimization with multiple velocity strategies and its application for p-xylene oxidation reaction process optimization. Chemom Intell Lab Syst 139:15–25CrossRefGoogle Scholar
  50. Fan SKS, Lin Y, Fan C, Wang Y (2009) Process identification using a new component analysis model and particle swarm optimization. Chemom Intell Lab Syst 99:19–29CrossRefGoogle Scholar
  51. Fang W, Sun J, Chen H, Wu X (2016) A decentralized quantum-inspired particle swarm optimization algorithm with cellular structured population. Inf Sci 330:19–48CrossRefGoogle Scholar
  52. Fernandez-Martinez JL, Garcia-Gonzalo E (2011) Stochastic stability analysis of the linear continuous and discrete PSO models. IEEE Trans Evolut Comput 15(3):405–423CrossRefGoogle Scholar
  53. Fourie PC, Groenwold AA (2002) The particle swarm optimization algorithm in size and shape optimization. Struct Multidiscip Optim 23(4):259–267CrossRefGoogle Scholar
  54. Ganesh MR, Krishna R, Manikantan K, Ramachandran S (2014) Entropy based binary particle swarm optimization and classification for ear detection. Eng Appl Artif Intell 27:115–128CrossRefGoogle Scholar
  55. Garcia-Gonza E, Fernandez-Martinez JL (2014) Convergence and stochastic stability analysis of particle swarm optimization variants with generic parameter distributions. Appl Math Comput 249:286–302MathSciNetMATHGoogle Scholar
  56. Garcia-Martinez C, Rodriguez FJ (2012) Arbitrary function optimisation with metaheuristics: no free lunch and real-world problems. Soft Comput 16:2115–2133CrossRefGoogle Scholar
  57. Geng J, Li M, Dong Z, Liao Y (2014) Port throughput forecasting by MARS-RSVR with chaotic simulated annealing particle swarm optimization algorithm. Neurocomputing 147:239–250CrossRefGoogle Scholar
  58. Ghodratnama A, Jolai F, Tavakkoli-Moghaddamb R (2015) Solving a new multi-objective multiroute flexible flow line problem by multi-objective particle swarm optimization and nsga-ii. J Manuf Syst 36:189–202CrossRefGoogle Scholar
  59. Goldbarg EFG, de Souza GR, Goldbarg MC (2006) Particle swarm for the traveling salesman problem. In: Proceedings of European conference on evolutionary computation in combinatorial optimization (EvoCOP2006), pp 99-110, Budapest, Hungary, April 10–12, 2006Google Scholar
  60. Gosciniak I (2015) A new approach to particle swarm optimization algorithm. Expert Syst Appl 42:844–854CrossRefGoogle Scholar
  61. Hanaf I, Cabrerab FM, Dimanea F, Manzanaresb JT (2016) Application of particle swarm optimization for optimizing the process parameters in turning of peek cf30 composites. Procedia Technol 22:195–202CrossRefGoogle Scholar
  62. He S, Wu Q, Wen J (2004) A particle swarm optimizer with passive congregation. BioSystems 78:135–147CrossRefGoogle Scholar
  63. Hendtlass T (2003) Preserving diversity in particle swarm optimisation. In: Proceedings of the 16th international conference on industrial engineering applications of artificial intelligence and expert systems, pp 31–40, Loughborough, UK, June 23–26, 2003Google Scholar
  64. Ho S, Yang S, Ni G (2006) A particle swarm optimization method with enhanced global search ability for design optimizations of electromagnetic devices. IEEE Trans Magn 42(4):1107–1110CrossRefGoogle Scholar
  65. Hu X, Eberhart RC (2002) Adaptive particle swarm optimization: Detection and response to dynamic systems. In: Proceedings of IEEE congress on evolutionary computation, pp 1666–1670, Honolulu, HI, USA, May 10–14, 2002Google Scholar
  66. Huang T, Mohan AS (2005) A hybrid boundary condition for robust particle swarm optimization. Antennas Wirel Propag Lett 4:112–117CrossRefGoogle Scholar
  67. Ide A, Yasuda K (2005) A basic study of adaptive particle swarm optimization. Electr Eng Jpn 151(3):41–49CrossRefGoogle Scholar
  68. Ivatloo BM (2013) Combined heat and power economic dispatch problem solution using particle swarm optimization with time varying acceleration coefficients. Electr Power Syst Res 95(1):9–18CrossRefGoogle Scholar
  69. Jamian JJ, Mustafa MW, Mokhlis H (2015) Optimal multiple distributed generation output through rank evolutionary particle swarm optimization. Neurocomputing 152:190–198CrossRefGoogle Scholar
  70. Jia D, Zheng G, Qu B, Khan MK (2011) A hybrid particle swarm optimization algorithm for high-dimensional problems. Comput Ind Eng 61:1117–1122CrossRefGoogle Scholar
  71. Jian W, Xue Y, Qian J (2004) An improved particle swarm optimization algorithm with neighborhoods topologies. In: Proceedings of 2004 international conference on machine learning and cybernetics, pp 2332–2337, Shanghai, China, August 26–29, 2004Google Scholar
  72. Jiang CW, Bompard E (2005) A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimization. Math Comput Simul 68:57–65MATHCrossRefGoogle Scholar
  73. Jie J, Zeng J, Han C (2006) Adaptive particle swarm optimization with feedback control of diversity. In: Proceedings of 2006 international conference on intelligent computing (ICIC2006), pp 81–92, Kunming, China, August 16–19, 2006Google Scholar
  74. Jin Y, Cheng H, Yan J (2005) Local optimum embranchment based convergence guarantee particle swarm optimization and its application in transmission network planning. In: Proceedings of 2005 IEEE/PES transmission and distribution conference and exhibition: Asia and Pacific, pp 1–6, Dalian, China, Aug 15–18, 2005Google Scholar
  75. Juang YT, Tung SL, Chiu HC (2011) Adaptive fuzzy particle swarm optimization for global optimization of multimodal functions. Inf Sci 181:4539–4549MathSciNetMATHCrossRefGoogle Scholar
  76. Kadirkamanathan V, Selvarajah K, Fleming PJ (2006) Stability analysis of the particle dynamics in particle swarm optimizer. IEEE Trans Evolut Comput 10(3):245–255CrossRefGoogle Scholar
  77. Kennedy J (1997) Minds and cultures: particle swarm implications. In: Proceedings of the AAAI Fall 1997 symposium on communicative action in humans and machines, pp 67–72, Cambridge, MA, USA, Nov 8–10, 1997Google Scholar
  78. Kennedy J (1998) The behavior of particle. In: Proceedings of the 7th annual conference on evolutionary program, pp 581–589, San Diego, CA, Mar 10–13, 1998Google Scholar
  79. Kennedy J (1999) Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of the IEEE international conference on evolutionary computation, pp 1931–1938, San Diego, CA, Mar 10–13Google Scholar
  80. Kennedy J (2000) Stereotyping: Improving particle swarm performance with cluster analysis. In: Proceedings of the IEEE international conference on evolutionary computation, pp 303–308Google Scholar
  81. Kennedy J (2003) Bare bones particle swarms. In: Proceedings of the 2003 IEEE swarm intelligence symposium (SIS’03), pp 80–87, Indianapolis, IN, USA, April 24–26, 2003Google Scholar
  82. Kennedy J (2004) Probability and dynamics in the particle swarm. In: Proceedings of the IEEE international conference on evolutionary computation, pp 340–347, Washington, DC, USA, July 6–9, 2004Google Scholar
  83. Kennedy J (2005) Why does it need velocity? In: Proceedings of the IEEE swarm intelligence symposium (SIS’05), pp 38–44, Pasadena, CA, USA, June 8–10, 2005Google Scholar
  84. Kennedy J, Eberhart RC (1995) Particle swarm optimization? In: Proceedings of the IEEE international conference on neural networks, pp 1942–1948, Perth, AustraliaGoogle Scholar
  85. Kennedy J, Mendes R (2002) Population structure and particle swarm performance. In: Proceedings of the IEEE international conference on evolutionary computation, pp 1671–1676, Honolulu, HI, USA, Sept 22–25, 2002Google Scholar
  86. Kennedy J, Mendes R (2003) Neighborhood topologies in fully-informed and best-of-neighborhood particle swarms. In: Proceedings of the 2003 IEEE international workshop on soft computing in industrial applications (SMCia/03), pp 45–50, Binghamton, New York, USA, Oct 12–14, 2003Google Scholar
  87. Krink T, Lovbjerg M (2002) The life cycle model: combining particle swarm optimisation, genetic algorithms and hillclimbers. In: Lecture notes in computer science (LNCS) No. 2439: proceedings of parallel problem solving from nature VII (PPSN 2002), pp 621–630, Granada, Spain, 7–11 Dec 2002Google Scholar
  88. Lee S, Soak S, Oh S, Pedrycz W, Jeonb M (2008) Modified binary particle swarm optimization. Prog Nat Sci 18:1161–1166MathSciNetCrossRefGoogle Scholar
  89. Lei K, Wang F, Qiu Y (2005) An adaptive inertia weight strategy for particle swarm optimizer. In: Proceedings of the third international conference on mechatronics and information technology, pp 51–55, Chongqing, China, Sept 21–24, 2005Google Scholar
  90. Leontitsis A, Kontogiorgos D, Pagge J (2006) Repel the swarm to the optimum. Appl Math Comput 173(1):265–272MathSciNetMATHGoogle Scholar
  91. Li X (2004) Better spread and convergence: particle swarm multiobjective optimization using the maximin fitness function. In: Proceedings of genetic and evolutionary computation conference (GECCO2004), pp 117–128, Seattle, WA, USA, June 26–30, 2004Google Scholar
  92. Li X (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evolut Comput 14(1):150–169Google Scholar
  93. Li X, Dam KH (2003) Comparing particle swarms for tracking extrema in dynamic environments. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC’03), pp 1772–1779, Canberra, Australia, Dec 8–12, 2003Google Scholar
  94. Li Z, Wang W, Yan Y, Li Z (2011) PS-ABC: a hybrid algorithm based on particle swarm and artificial bee colony for high-dimensional optimization problems. Expert Syst Appl 42:8881–8895CrossRefGoogle Scholar
  95. Li C, Yang S, Nguyen TT (2012) A self-learning particle swarm optimizer for global optimization problems. IEEE Trans Syst Man Cybernet Part B Cybernet 42(3):627–646CrossRefGoogle Scholar
  96. Li Y, Zhan Z, Lin S, Zhang J, Luo X (2015a) Competitive and cooperative particle swarm optimization with information sharing mechanism for global optimization problems. Inf Sci 293:370–382CrossRefGoogle Scholar
  97. Li Z, Nguyena TT, Chen S, Khac Truong T (2015b) A hybrid algorithm based on particle swarm and chemical reaction optimization for multi-object problems. Appl Soft Comput 35:525–540CrossRefGoogle Scholar
  98. Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer. In: Proceedings of IEEE swarm intelligence symposium, pp 124–129, Pasadena, CA, USA, June 8–10, 2005Google Scholar
  99. Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evolut Comput 10(3):281–295CrossRefGoogle Scholar
  100. Lim W, Isa NAM (2014) Particle swarm optimization with adaptive time-varying topology connectivity. Appl Soft Comput 24:623–642CrossRefGoogle Scholar
  101. Lim W, Isa NAM (2015) Adaptive division of labor particle swarm optimization. Expert Syst Appl 42:5887–5903CrossRefGoogle Scholar
  102. Lin Q, Li J, Du Z, Chen J, Ming Z (2006a) A novel multi-objective particle swarm optimization with multiple search strategies. Eur J Oper Res 247:732–744MathSciNetMATHCrossRefGoogle Scholar
  103. Lin X, Li A, Chen B (2006b) Scheduling optimization of mixed model assembly lines with hybrid particle swarm optimization algorithm. Ind Eng Manag 11(1):53–57Google Scholar
  104. Liu Y, Qin Z, Xu Z (2004) Using relaxation velocity update strategy to improve particle swarm optimization. Proceedings of third international conference on machine learning and cybernetics, pp 2469–2472, Shanghai, China, August 26–29, 2004Google Scholar
  105. Liu F, Zhou J, Fang R (2005) An improved particle swarm optimization and its application in longterm stream ow forecast. In: Proceedings of 2005 international conference on machine learning and cybernetics, pp 2913–2918, Guangzhou, China, August 18–21, 2005Google Scholar
  106. Liu H, Yang G, Song G (2014) MIMO radar array synthesis using QPSO with normal distributed contraction-expansion factor. Procedia Eng 15:2449–2453CrossRefGoogle Scholar
  107. Liu T, Jiao L, Ma W, Ma J, Shang R (2016) A new quantum-behaved particle swarm optimization based on cultural evolution mechanism for multiobjective problems. Knowl Based Syst 101:90–99CrossRefGoogle Scholar
  108. Lovbjerg M, Krink T (2002) Extending particle swarm optimizers with self-organized criticality. In: Proceedings of IEEE congress on evolutionary computation (CEC 2002), pp 1588–1593, Honolulu, HI, USA, May 7–11, 2002Google Scholar
  109. Lovbjerg M, Rasmussen TK, Krink T (2001) Hybrid particle swarm optimizer with breeding and subpopulations. In: Proceedings of third genetic and evolutionary computation conference (GECCO-2001), pp 469–476, San Francisco-Silicon Valley, CA, USA, July 7–11, 2001Google Scholar
  110. Lu J, Hu H, Bai Y (2015a) Generalized radial basis function neural network based on an improved dynamic particle swarm optimization and adaboost algorithm. Neurocomputing 152:305–315CrossRefGoogle Scholar
  111. Lu Y, Zeng N, Liu Y, Zhang Z (2015b) A hybrid wavelet neural network and switching particle swarm optimization algorithm for face direction recognition. Neurocomputing 155:219–244CrossRefGoogle Scholar
  112. Medasani S, Owechko Y (2005) Possibilistic particle swarms for optimization. In: Applications of neural networks and machine learning in image processing IX vol 5673, pp 82–89Google Scholar
  113. Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler maybe better. IEEE Trans Evolut Comput 8(3):204–210CrossRefGoogle Scholar
  114. Meng A, Li Z, Yin H, Chen S, Guo Z (2015) Accelerating particle swarm optimization using crisscross search. Inf Sci 329:52–72CrossRefGoogle Scholar
  115. Mikki S, Kishk A (2005) Improved particle swarm optimization technique using hard boundary conditions. Microw Opt Technol Lett 46(5):422–426CrossRefGoogle Scholar
  116. Mohais AS, Mendes R, Ward C (2005) Neighborhood re-structuring in particle swarm optimization. In: Proceedings of Australian conference on artificial intelligence, pp 776–785, Sydney, Australia, Dec 5–9, 2005Google Scholar
  117. Monson CK, Seppi KD (2004) The Kalman swarm: a new approach to particle motion in swarm optimization. In: Proceedings of genetic and evolutionary computation conference (GECCO2004), pp 140–150, Seattle, WA, USA, June 26–30, 2004Google Scholar
  118. Monson CK, Seppi KD (2005) Bayesian optimization models for particle swarms. In: Proceedings of genetic and evolutionary computation conference (GECCO2005), pp 193–200, Washington, DC, USA, June 25–29, 2005Google Scholar
  119. Mostaghim S, Teich J (2003) Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of the 2003 IEEE swarm intelligence symposium (SIS’03), pp 26–33, Indianapolis, Indiana, USA, April 24–26, 2003Google Scholar
  120. Mu B, Wen S, Yuan S, Li H (2015) PPSO: PCA based particle swarm optimization for solving conditional nonlinear optimal perturbation. Comput Geosci 83:65–71CrossRefGoogle Scholar
  121. Netjinda N, Achalakul T, Sirinaovakul B (2015) Particle swarm optimization inspired by starling flock behavior. Appl Soft Comput 35:411–422CrossRefGoogle Scholar
  122. Ngoa TT, Sadollahb A, Kima JH (2016) A cooperative particle swarm optimizer with stochastic movements for computationally expensive numerical optimization problems. J Comput Sci 13:68–82MathSciNetCrossRefGoogle Scholar
  123. Nickabadi AA, Ebadzadeh MM, Safabakhsh R (2011) A novel particle swarm optimization algorithm with adaptive inertia weight. Appl Soft Comput 11:3658–3670CrossRefGoogle Scholar
  124. Niu B, Zhu Y, He X (2005) Multi-population cooperative particle swarm optimization. In: Proceedings of advances in artificial life—the eighth European conference (ECAL 2005), pp 874–883, Canterbury, UK, Sept 5–9, 2005Google Scholar
  125. Noel MM, Jannett TC (2004) Simulation of a new hybrid particle swarm optimization algorithm. In: Proceedings of the thirty-sixth IEEE Southeastern symposium on system theory, pp 150–153, Atlanta, Georgia, USA, March 14–16, 2004Google Scholar
  126. Ozcan E, Mohan CK (1998) Analysis of a simple particle swarm optimization system. In: Intelligent engineering systems through artificial neural networks, pp 253–258Google Scholar
  127. Pampara G, Franken N, Engelbrecht AP (2005) Combining particle swarm optimization with angle modulation to solve binary problems. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 89–96, Edinburgh, UK, Sept 2–4, 2005Google Scholar
  128. Park JB, Jeong YW, Shin JR, Lee KY (2010) An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans Power Syst 25(1):156–166CrossRefGoogle Scholar
  129. Parsopoulos KE, Vrahatis MN (2002a) Initializing the particle swarm optimizer using the nonlinear simplex method. WSEAS Press, RomeMATHGoogle Scholar
  130. Parsopoulos KE, Vrahatis MN (2002b) Recent approaches to global optimization problems through particle swarm optimization. Nat Comput 1:235–306MathSciNetMATHCrossRefGoogle Scholar
  131. Parsopoulos KE, Vrahatis MN (2004) On the computation of all global minimizers through particle swarm optimization. IEEE Trans Evolut Comput 8(3):211–224CrossRefGoogle Scholar
  132. Peer E, van den Bergh F, Engelbrecht AP (2003) Using neighborhoods with the guaranteed convergence PSO. In: Proceedings of IEEE swarm intelligence symposium (SIS2003), pp 235–242, Indianapolis, IN, USA, April 24–26, 2003Google Scholar
  133. Peng CC, Chen CH (2015) Compensatory neural fuzzy network with symbiotic particle swarm optimization for temperature control. Appl Math Model 39:383–395CrossRefGoogle Scholar
  134. Peram T, Veeramachaneni k, Mohan CK (2003) Fitness-distance-ratio based particle swarm optimization. In: Proceedings of 2003 IEEE swarm intelligence symposium, pp 174–181, Indianapolis, Indiana, USA, April 24–26, 2003Google Scholar
  135. Poli R (2008) Dynamics and stability of the sampling distribution of particle swarm optimisers via moment analysis. J Artif Evol Appl 10–34:2008Google Scholar
  136. Poli R (2009) Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. IEEE Trans Evolut Comput 13(4):712–721CrossRefGoogle Scholar
  137. Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization—an overview. Swarm Intell 1(1):33–57CrossRefGoogle Scholar
  138. Qian X, Cao M, Su Z, Chen J (2012) A hybrid particle swarm optimization (PSO)-simplex algorithm for damage identification of delaminated beams. Math Probl Eng 1–11:2012MathSciNetMATHGoogle Scholar
  139. Qin Z, Yu F, Shi Z (2006) Adaptive inertia weight particle swarm optimization. In: Proceedings of the genetic and evolutionary computation conference, pp 450–459, Zakopane, Poland, June 25–29, 2006Google Scholar
  140. Ratnaweera A, Halgamuge S, Watson H (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evolut Comput 8(3):240–255CrossRefGoogle Scholar
  141. Reynolds CW (1987) Flocks, herds, and schools: a distributed behavioral model. Comput Graph 21(4):25–34CrossRefGoogle Scholar
  142. Richards M, Ventura D (2004) Choosing a starting configuration for particle swarm optimization. In: Proceedings of 2004 IEEE international joint conference on neural networks, pp 2309–2312, Budapest, Hungary, July 25–29, 2004Google Scholar
  143. Richer TJ, Blackwell TM (2006) The levy particle swarm. In: Proceedings of the IEEE congress on evolutionary computation, pp 808–815, Vancouver, BC, Canada, July 16–21, 2006Google Scholar
  144. Riget J, Vesterstrom JS (2002) A diversity-guided particle swarm optimizer—the ARPSO.Technical Report 2002-02, Department of Computer Science, Aarhus University, Aarhus, DenmarkGoogle Scholar
  145. Robinson J, Rahmat-Samii Y (2004) Particle swarm optimization in electromagnetics. IEEE Trans Antennas Propag 52(2):397–407MathSciNetMATHCrossRefGoogle Scholar
  146. Robinson J, Sinton S, Rahmat-Samii Y (2002) Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. In: Proceedings of 2002 IEEE international symposium on antennas propagation, pp 31–317, San Antonio, Texas, USA, June 16–21, 2002Google Scholar
  147. Roy R, Ghoshal SP (2008) A novel crazy swarm optimized economic load dispatch for various types of cost functions. Electr Power Energy Syst 30:242–253CrossRefGoogle Scholar
  148. Salehian S, Subraminiam SK (2015) Unequal clustering by improved particle swarm optimization in wireless sensor network. Procedia Comput Sci 62:403–409Google Scholar
  149. Samuel GG, Rajan CCA (2015) Hybrid: particle swarm optimization-genetic algorithm and particle swarm optimization-shuffled frog leaping algorithm for long-term generator maintenance scheduling. Electr Power Energy Syst 65:432–442CrossRefGoogle Scholar
  150. Schaffer JD (1985) Multi objective optimization with vector evaluated genetic algorithms. In: Proceedings of the IEEE international conference on genetic algorithm, pp 93–100, Pittsburgh, Pennsylvania, USAGoogle Scholar
  151. Schoeman IL, Engelbrecht AP (2005) A parallel vector-based particle swarm optimizer. In: Proceedings of the international conference on neural networks and genetic algorithms (ICANNGA 2005), pp 268–271, ProtugalGoogle Scholar
  152. Schutte JF, Groenwold AA (2005) A study of global optimization using particle swarms. J Glob Optim 31:93–108MathSciNetMATHCrossRefGoogle Scholar
  153. Selleri S, Mussetta M, Pirinoli P (2006) Some insight over new variations of the particle swarm optimization method. IEEE Antennas Wirel Propag Lett 5(1):235–238CrossRefGoogle Scholar
  154. Selvakumar AI, Thanushkodi K (2009) Optimization using civilized swarm: solution to economic dispatch with multiple minima. Electr Power Syst Res 79:8–16CrossRefGoogle Scholar
  155. Seo JH, Im CH, Heo CG (2006) Multimodal function optimization based on particle swarm optimization. IEEE Trans Magn 42(4):1095–1098CrossRefGoogle Scholar
  156. Sharifi A, Kordestani JK, Mahdaviania M, Meybodi MR (2015) A novel hybrid adaptive collaborative approach based on particle swarm optimization and local search for dynamic optimization problems. Appl Soft Comput 32:432–448CrossRefGoogle Scholar
  157. Shelokar PS, Siarry P, Jayaraman VK, Kulkarni BD (2007) Particle swarm and ant colony algorithms hybridized for improved continuous optimization. Appl Math Comput 188:129–142MathSciNetMATHGoogle Scholar
  158. Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE international conference on evolutionary computation, pp 69–73, Anchorage, Alaska, USA, May 4–9, 1998Google Scholar
  159. Shi Y, Eberhart RC (2001) Fuzzy adaptive particle swarm optimization. In: Proceedings of the congress on evolutionary computation, pp 101–106, IEEE Service Center, Seoul, Korea, May 27–30, 2001Google Scholar
  160. Shin Y, Kita E (2014) Search performance improvement of particle swarm optimization by second best particle information. Appl Math Comput 246:346–354MathSciNetMATHGoogle Scholar
  161. Shirkhani R, Jazayeri-Rad H, Hashemi SJ (2014) Modeling of a solid oxide fuel cell power plant using an ensemble of neural networks based on a combination of the adaptive particle swarm optimization and levenberg marquardt algorithms. J Nat Gas Sci Eng 21:1171–1183CrossRefGoogle Scholar
  162. Sierra MR, Coello CAC (2005) Improving pso-based multi-objective optimization using crowding, mutation and epsilon-dominance. Lect Notes Comput Sci 3410:505–519MATHCrossRefGoogle Scholar
  163. Soleimani H, Kannan G (2015) A hybrid particle swarm optimization and genetic algorithm for closedloop supply chain network design in large-scale networks. Appl Math Model 39:3990–4012MathSciNetCrossRefGoogle Scholar
  164. Stacey A, Jancic M, Grundy I (2003) Particle swarm optimization with mutation. In: Proceedings of IEEE congress on evolutionary computation 2003 (CEC 2003), pp 1425–1430, Canberra, Australia, December 8–12, 2003Google Scholar
  165. Suganthan PN (1999) Particle swarm optimizer with neighborhood operator. In: Proceedings of the Congress on Evolutionary Computation, pp 1958–1962, Washington, D.C. USA, July 6–9, 1999Google Scholar
  166. Sun J, Feng B, Xu W (2004) Particle swarm optimization with particles having quantum behavior. In: Proceedings of the congress on evolutionary computation, pp 325–331, Portland, OR, USA, June 19–23, 2004Google Scholar
  167. Tang Y, Wang Z, Fang J (2011) Feedback learning particle swarm optimization. Appl Soft Comput 11:4713–4725CrossRefGoogle Scholar
  168. Tanweer MR, Suresh S, Sundararajan N (2016) Dynamic mentoring and self-regulation based particle swarm optimization algorithm for solving complex real-world optimization problems. Inf Sci 326:1–24CrossRefGoogle Scholar
  169. Tatsumi K, Ibuki T, Tanino T (2013) A chaotic particle swarm optimization exploiting a virtual quartic objective function based on the personal and global best solutions. Appl Math Comput 219(17):8991–9011MathSciNetMATHGoogle Scholar
  170. Tatsumi K, Ibuki T, Tanino T (2015) Particle swarm optimization with stochastic selection of perturbation-based chaotic updating system. Appl Math Comput 269:904–929MathSciNetGoogle Scholar
  171. Ting T, Rao MVC, Loo CK (2003) A new class of operators to accelerate particle swarm optimization. In: Proceedings of IEEE congress on evolutionary computation 2003(CEC2003), pp 2406–2410, Canberra, Australia, Dec 8–12, 2003Google Scholar
  172. Trelea IC (2003) The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf Process Lett 85(6):317–325MathSciNetMATHCrossRefGoogle Scholar
  173. Tsafarakis S, Saridakis C, Baltas G, Matsatsinis N (2013) Hybrid particle swarm optimization with mutation for optimizing industrial product lines: an application to a mixed solution space considering both discrete and continuous design variables. Ind Market Manage 42(4):496–506CrossRefGoogle Scholar
  174. van den Bergh F (2001) An analysis of particle swarm optimizers. Ph.D. dissertation, University of Pretoria, Pretoria, South AfricaGoogle Scholar
  175. van den Bergh F, Engelbrecht AP (2002) A new locally convergent particle swarm optimizer. In: Proceedings of IEEE conference on system, man and cybernetics, pp 96–101, Hammamet, Tunisia, October, 2002Google Scholar
  176. van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evolut Comput 8(3):225–239CrossRefGoogle Scholar
  177. van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176:937–971MathSciNetMATHCrossRefGoogle Scholar
  178. Vitorino LN, Ribeiro SF, Bastos-Filho CJA (2015) A mechanism based on artificial bee colony to generate diversity in particle swarm optimization. Neurocomputing 148:39–45CrossRefGoogle Scholar
  179. Vlachogiannis JG, Lee KY (2009) Economic load dispatch—a comparative study on heuristic optimization techniques with an improved coordinated aggregation based pso. IEEE Trans Power Syst 24(2):991–1001CrossRefGoogle Scholar
  180. Wang W (2012) Research on particle swarm optimization algorithm and its application. Southwest Jiaotong University, Doctor Degree Dissertation, pp 36–37Google Scholar
  181. Wang Q, Wang Z, Wang S (2005) A modified particle swarm optimizer using dynamic inertia weight. China Mech Eng 16(11):945–948Google Scholar
  182. Wang H, Wu Z, Rahnamayan S, Liu Y, Ventresca M (2011) Enhancing particle swarm optimization using generalized opposition-based learning. Inf Sci 181:4699–4714MathSciNetCrossRefGoogle Scholar
  183. Wang H, Sun H, Li C, Rahnamayan S, Pan J (2013) Diversity enhanced particle swarm optimization with neighborhood search. Inf Sci 223:119–135MathSciNetCrossRefGoogle Scholar
  184. Wen W, Liu G (2005) Swarm double-tabu search. In: First international conference on intelligent computing, pp 1231–1234, Changsha, China, August 23–26, 2005Google Scholar
  185. Wolpert DH, Macready WG (1997) Free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67–82CrossRefGoogle Scholar
  186. Xie X, Zhang W, Yang Z (2002) A dissipative particle swarm optimization. In: Proceedings of IEEE congression on evolutionary computation, pp 1456–1461, Honolulu, HI, USA, May, 2002Google Scholar
  187. Xie X, Zhang W, Bi D (2004) Optimizing semiconductor devices by self-organizing particle swarm. In: Proceedings of congress on evolutionary computation (CEC2004), pp 2017–2022, Portland, Oregon, USA, June 19–23, 2004Google Scholar
  188. Yang C, Simon D (2005) A new particle swarm optimization technique. In: Proceedings of 17th international conference on systems engineering (ICSEng 2005), pp 164–169, Las Vegas, Nevada, USA, Aug 16–18, 2005Google Scholar
  189. Yang Z, Wang F (2006) An analysis of roulette selection in early particle swarm optimizing. In: Proceedings of the 1st international symposium on systems and control in aerospace and astronautics, (ISSCAA 2006), pp 960–970, Harbin, China, Jan 19–21, 2006Google Scholar
  190. Yang X, Yuan J, Yuan J, Mao H (2007) A modified particle swarm optimizer with dynamic adaptation. Appl Math Comput 189:1205–1213MathSciNetMATHGoogle Scholar
  191. Yang C, Gao W, Liu N, Song C (2015) Low-discrepancy sequence initialized particle swarm optimization algorithm with high-order nonlinear time-varying inertia weight. Appl Soft Comput 29:386–394CrossRefGoogle Scholar
  192. Yasuda K, Ide A, Iwasaki N (2003) Adaptive particle swarm optimization. In: Proceedings of IEEE international conference on systems, man and cybernetics, pp 1554–1559, Washington, DC, USA, October 5–8, 2003Google Scholar
  193. Yasuda K, Iwasaki N (2004) Adaptive particle swarm optimization using velocity information of swarm. In: Proceedings of IEEE international conference on systems, man and cybernetics, pp 3475–3481, Hague, Netherlands, October 10–13, 2004Google Scholar
  194. Yu H, Zhang L, Chen D, Song X, Hu S (2005) Estimation of model parameters using composite particle swarm optimization. J Chem Eng Chin Univ 19(5):675–680Google Scholar
  195. Yuan Y, Ji B, Yuan X, Huang Y (2015) Lockage scheduling of three gorges-gezhouba dams by hybrid of chaotic particle swarm optimization and heuristic-adjusted strategies. Appl Math Comput 270:74–89MathSciNetGoogle Scholar
  196. Zeng J, Cui Z, Wang L (2005) A differential evolutionary particle swarm optimization with controller. In: Proceedings of the first international conference on intelligent computing (ICIC 2005), pp 467–476, Hefei, China, Aug 23–25, 2005Google Scholar
  197. Zhai S, Jiang T (2015) A new sense-through-foliage target recognition method based on hybrid differential evolution and self-adaptive particle swarm optimization-based support vector machine. Neurocomputing 149:573–584CrossRefGoogle Scholar
  198. Zhan Z, Zhang J, Li Y, Chung HH (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybernet Part B Cybernet 39(6):1362–1381CrossRefGoogle Scholar
  199. Zhan Z, Zhang J, Li Y, Shi Y (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evolut Comput 15(6):832–847Google Scholar
  200. Zhang L, Yu H, Hu S (2003) A new approach to improve particle swarm optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference 2003 (GECCO 2003), pp 134–139, Chicago, IL, USA, July 12–16, 2003Google Scholar
  201. Zhang R, Zhou J, Moa L, Ouyanga S, Liao X (2013) Economic environmental dispatch using an enhanced multi-objective cultural algorithm. Electr Power Syst Res 99:18–29CrossRefGoogle Scholar
  202. Zhang L, Tang Y, Hua C, Guan X (2015) A new particle swarm optimization algorithm with adaptive inertia weight based on bayesian techniques. Appl Soft Comput 28:138–149CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Electrical EngineeringZhengzhou UniversityZhengzhouChina
  2. 2.Department of ResearchThe People’s Bank of China, Zhengzhou Central Sub-BranchZhengzhouChina

Personalised recommendations