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Particle swarm optimization algorithm: an overview

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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.

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References

  • 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 1086–1091

  • 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 1875–1882

  • 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 217–220

  • 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 489–494

  • al Rifaie MM, Blackwell T (2012) Bare bones particle swarms with jumps ants. Lect Notes Comput Sci Ser 7461(1):49–60

    Article  Google Scholar 

  • 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, Berlin

  • 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 84–89

  • Ardizzon G, Cavazzini G, Pavesi G (2015) Adaptive acceleration coefficients for a new search diversification strategy in particle swarm optimization algorithms. Inf Sci 299:337–378

    Article  Google Scholar 

  • 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 52:94–100

    Article  Google Scholar 

  • Barisal AK (2013) Dynamic search space squeezing strategy based intelligent algorithm solutions to economic dispatch with multiple fuels. Electr Power Energy Syst 45:50–59

    Article  Google Scholar 

  • 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 Science

  • 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 Science

  • 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 34–37

  • Beheshti Z, Shamsuddin SM (2015) Non-parametric particle swarm optimization for global optimization. Appl Soft Comput 28:345–359

    Article  Google Scholar 

  • 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 3–9

  • 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 45–52

  • Blackwell TM (2005) Particle swarms and population diversity. Soft Comput 9(11):793–802

    Article  MATH  Google Scholar 

  • 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 1691–1697

  • 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 120–127

  • 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 1–9

  • 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 228–234

  • 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 429–434

  • Carlisle A, Dozier G (2001) An off-the-shelf PSO. In: Proceedings of the workshop on particle swarm optimization, Indianapolis, Indiana, USA

  • Chang WD (2015) A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems. Appl Soft Comput 33:170–182

    Article  Google Scholar 

  • Chatterjee A, Siarry P (2006) Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Comput Oper Res 33:859–871

    Article  MATH  Google Scholar 

  • Chaturvedi KT, Pandit M, Shrivastava L (2008) Self-organizing hierarchical particle swarm optimization for non-convex economic dispatch. IEEE Trans Power Syst 23(3):1079–1087

    Article  Google Scholar 

  • Chen J, Pan F, Cai T (2006a) Acceleration factor harmonious particle swarm optimizer. Int J Autom Comput 3(1):41–46

    Article  Google Scholar 

  • Chen K, Li T, Cao T (2006b) Tribe-PSO: a novel global optimization algorithm and its application in molecular docking. Chemom Intell Lab Syst 82:248–259

    Article  Google Scholar 

  • 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):241–258

    Article  Google Scholar 

  • Chen Y, Feng Y, Li X (2014) A parallel system for adaptive optics based on parallel mutation PSO algorithm. Optik 125:329–332

    Article  Google Scholar 

  • Ciuprina G, Ioan D, Munteanu I (2007) Use of intelligent-particle swarm optimization in electromagnetics. IEEE Trans Manag 38(2):1037–1040

    Google Scholar 

  • 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, 1999

  • Clerc M (2004) Discrete particle swarm optimization. In: Onwubolu GC (ed) New optimization techniques in engineering. Springer, Berlin

  • 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, 2006

  • Clerc M, Kennedy J (2002) The particle swarm-explosion, stability and convergence in a multi dimensional complex space. IEEE Trans Evolut Comput 6(2):58–73

    Article  Google Scholar 

  • 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 30:297–307

    Article  Google Scholar 

  • Coello CAC, Pulido G, Lechuga M (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evolut Comput 8(3):256–279

    Article  Google Scholar 

  • Deb K, Pratap A (2002) A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE Trans Evolut Comput 6(2):182–197

    Article  Google Scholar 

  • 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 12:171–195

    Article  Google Scholar 

  • 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, 2006

  • 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, 2005

  • 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, 1995

  • 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, 2000

  • 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 27–30

  • El-Wakeel AS (2014) Design optimization of pm couplings using hybrid particle swarm optimization-simplex method (PSO-SM) algorithm. Electr Power Syst Res 116:29–35

    Article  Google Scholar 

  • 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, 2004

  • 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, 2005

  • Fan H (2002) A modification to particle swarm optimization algorithm. Eng Comput 19(8):970–989

    Article  MATH  Google Scholar 

  • 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 139:15–25

    Article  Google Scholar 

  • 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 99:19–29

    Article  Google Scholar 

  • Fang W, Sun J, Chen H, Wu X (2016) A decentralized quantum-inspired particle swarm optimization algorithm with cellular structured population. Inf Sci 330:19–48

    Article  Google Scholar 

  • Fernandez-Martinez JL, Garcia-Gonzalo E (2011) Stochastic stability analysis of the linear continuous and discrete PSO models. IEEE Trans Evolut Comput 15(3):405–423

    Article  Google Scholar 

  • Fourie PC, Groenwold AA (2002) The particle swarm optimization algorithm in size and shape optimization. Struct Multidiscip Optim 23(4):259–267

    Article  Google Scholar 

  • Ganesh MR, Krishna R, Manikantan K, Ramachandran S (2014) Entropy based binary particle swarm optimization and classification for ear detection. Eng Appl Artif Intell 27:115–128

    Article  Google Scholar 

  • Garcia-Gonza E, Fernandez-Martinez JL (2014) Convergence and stochastic stability analysis of particle swarm optimization variants with generic parameter distributions. Appl Math Comput 249:286–302

    MathSciNet  MATH  Google Scholar 

  • Garcia-Martinez C, Rodriguez FJ (2012) Arbitrary function optimisation with metaheuristics: no free lunch and real-world problems. Soft Comput 16:2115–2133

    Article  Google Scholar 

  • Geng J, Li M, Dong Z, Liao Y (2014) Port throughput forecasting by MARS-RSVR with chaotic simulated annealing particle swarm optimization algorithm. Neurocomputing 147:239–250

    Article  Google Scholar 

  • 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 36:189–202

    Article  Google Scholar 

  • 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, 2006

  • Gosciniak I (2015) A new approach to particle swarm optimization algorithm. Expert Syst Appl 42:844–854

    Article  Google Scholar 

  • 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 22:195–202

    Article  Google Scholar 

  • He S, Wu Q, Wen J (2004) A particle swarm optimizer with passive congregation. BioSystems 78:135–147

    Article  Google Scholar 

  • 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, 2003

  • 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):1107–1110

    Article  Google Scholar 

  • 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, 2002

  • Huang T, Mohan AS (2005) A hybrid boundary condition for robust particle swarm optimization. Antennas Wirel Propag Lett 4:112–117

    Article  Google Scholar 

  • Ide A, Yasuda K (2005) A basic study of adaptive particle swarm optimization. Electr Eng Jpn 151(3):41–49

    Article  Google Scholar 

  • 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):9–18

    Article  Google Scholar 

  • Jamian JJ, Mustafa MW, Mokhlis H (2015) Optimal multiple distributed generation output through rank evolutionary particle swarm optimization. Neurocomputing 152:190–198

    Article  Google Scholar 

  • Jia D, Zheng G, Qu B, Khan MK (2011) A hybrid particle swarm optimization algorithm for high-dimensional problems. Comput Ind Eng 61:1117–1122

    Article  Google Scholar 

  • 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, 2004

  • Jiang CW, Bompard E (2005) A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimization. Math Comput Simul 68:57–65

    Article  MATH  Google Scholar 

  • 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, 2006

  • 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, 2005

  • Juang YT, Tung SL, Chiu HC (2011) Adaptive fuzzy particle swarm optimization for global optimization of multimodal functions. Inf Sci 181:4539–4549

    Article  MathSciNet  MATH  Google Scholar 

  • Kadirkamanathan V, Selvarajah K, Fleming PJ (2006) Stability analysis of the particle dynamics in particle swarm optimizer. IEEE Trans Evolut Comput 10(3):245–255

    Article  Google Scholar 

  • 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, 1997

  • 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, 1998

  • 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 10–13

  • Kennedy J (2000) Stereotyping: Improving particle swarm performance with cluster analysis. In: Proceedings of the IEEE international conference on evolutionary computation, pp 303–308

  • 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, 2003

  • 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, 2004

  • 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, 2005

  • Kennedy J, Eberhart RC (1995) Particle swarm optimization? In: Proceedings of the IEEE international conference on neural networks, pp 1942–1948, Perth, Australia

  • 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, 2002

  • 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, 2003

  • 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 2002

  • Lee S, Soak S, Oh S, Pedrycz W, Jeonb M (2008) Modified binary particle swarm optimization. Prog Nat Sci 18:1161–1166

    Article  MathSciNet  Google Scholar 

  • 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, 2005

  • Leontitsis A, Kontogiorgos D, Pagge J (2006) Repel the swarm to the optimum. Appl Math Comput 173(1):265–272

    MathSciNet  MATH  Google Scholar 

  • 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, 2004

  • Li X (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evolut Comput 14(1):150–169

  • 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, 2003

  • 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 42:8881–8895

    Article  Google Scholar 

  • 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):627–646

    Article  Google Scholar 

  • 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 293:370–382

    Article  Google Scholar 

  • 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 35:525–540

    Article  Google Scholar 

  • 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, 2005

  • 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):281–295

    Article  Google Scholar 

  • Lim W, Isa NAM (2014) Particle swarm optimization with adaptive time-varying topology connectivity. Appl Soft Comput 24:623–642

    Article  Google Scholar 

  • Lim W, Isa NAM (2015) Adaptive division of labor particle swarm optimization. Expert Syst Appl 42:5887–5903

    Article  Google Scholar 

  • 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 247:732–744

    Article  MathSciNet  MATH  Google Scholar 

  • 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):53–57

    Google Scholar 

  • 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, 2004

  • 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, 2005

  • Liu H, Yang G, Song G (2014) MIMO radar array synthesis using QPSO with normal distributed contraction-expansion factor. Procedia Eng 15:2449–2453

    Article  Google Scholar 

  • 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 101:90–99

    Article  Google Scholar 

  • 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, 2002

  • 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, 2001

  • 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 152:305–315

    Article  Google Scholar 

  • 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 155:219–244

    Article  Google Scholar 

  • 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 82–89

  • Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler maybe better. IEEE Trans Evolut Comput 8(3):204–210

    Article  Google Scholar 

  • Meng A, Li Z, Yin H, Chen S, Guo Z (2015) Accelerating particle swarm optimization using crisscross search. Inf Sci 329:52–72

    Article  Google Scholar 

  • Mikki S, Kishk A (2005) Improved particle swarm optimization technique using hard boundary conditions. Microw Opt Technol Lett 46(5):422–426

    Article  Google Scholar 

  • 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, 2005

  • 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, 2004

  • 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, 2005

  • 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, 2003

  • Mu B, Wen S, Yuan S, Li H (2015) PPSO: PCA based particle swarm optimization for solving conditional nonlinear optimal perturbation. Comput Geosci 83:65–71

    Article  Google Scholar 

  • Netjinda N, Achalakul T, Sirinaovakul B (2015) Particle swarm optimization inspired by starling flock behavior. Appl Soft Comput 35:411–422

    Article  Google Scholar 

  • Ngoa TT, Sadollahb A, Kima JH (2016) A cooperative particle swarm optimizer with stochastic movements for computationally expensive numerical optimization problems. J Comput Sci 13:68–82

    Article  MathSciNet  Google Scholar 

  • Nickabadi AA, Ebadzadeh MM, Safabakhsh R (2011) A novel particle swarm optimization algorithm with adaptive inertia weight. Appl Soft Comput 11:3658–3670

    Article  Google Scholar 

  • 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, 2005

  • 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, 2004

  • Ozcan E, Mohan CK (1998) Analysis of a simple particle swarm optimization system. In: Intelligent engineering systems through artificial neural networks, pp 253–258

  • 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, 2005

  • 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):156–166

    Article  Google Scholar 

  • Parsopoulos KE, Vrahatis MN (2002a) Initializing the particle swarm optimizer using the nonlinear simplex method. WSEAS Press, Rome

    MATH  Google Scholar 

  • Parsopoulos KE, Vrahatis MN (2002b) Recent approaches to global optimization problems through particle swarm optimization. Nat Comput 1:235–306

    Article  MathSciNet  MATH  Google Scholar 

  • Parsopoulos KE, Vrahatis MN (2004) On the computation of all global minimizers through particle swarm optimization. IEEE Trans Evolut Comput 8(3):211–224

    Article  Google Scholar 

  • 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, 2003

  • Peng CC, Chen CH (2015) Compensatory neural fuzzy network with symbiotic particle swarm optimization for temperature control. Appl Math Model 39:383–395

    Article  Google Scholar 

  • 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, 2003

  • Poli R (2008) Dynamics and stability of the sampling distribution of particle swarm optimisers via moment analysis. J Artif Evol Appl 10–34:2008

    Google Scholar 

  • Poli R (2009) Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. IEEE Trans Evolut Comput 13(4):712–721

    Article  Google Scholar 

  • Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization—an overview. Swarm Intell 1(1):33–57

    Article  Google Scholar 

  • 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 1–11:2012

    MathSciNet  MATH  Google Scholar 

  • 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, 2006

  • Ratnaweera A, Halgamuge S, Watson H (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evolut Comput 8(3):240–255

    Article  Google Scholar 

  • Reynolds CW (1987) Flocks, herds, and schools: a distributed behavioral model. Comput Graph 21(4):25–34

    Article  Google Scholar 

  • 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, 2004

  • 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, 2006

  • Riget J, Vesterstrom JS (2002) A diversity-guided particle swarm optimizer—the ARPSO.Technical Report 2002-02, Department of Computer Science, Aarhus University, Aarhus, Denmark

  • Robinson J, Rahmat-Samii Y (2004) Particle swarm optimization in electromagnetics. IEEE Trans Antennas Propag 52(2):397–407

    Article  MathSciNet  MATH  Google Scholar 

  • 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, 2002

  • Roy R, Ghoshal SP (2008) A novel crazy swarm optimized economic load dispatch for various types of cost functions. Electr Power Energy Syst 30:242–253

    Article  Google Scholar 

  • Salehian S, Subraminiam SK (2015) Unequal clustering by improved particle swarm optimization in wireless sensor network. Procedia Comput Sci 62:403–409

  • 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 65:432–442

    Article  Google Scholar 

  • 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, USA

  • 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, Protugal

  • Schutte JF, Groenwold AA (2005) A study of global optimization using particle swarms. J Glob Optim 31:93–108

    Article  MathSciNet  MATH  Google Scholar 

  • 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):235–238

    Article  Google Scholar 

  • Selvakumar AI, Thanushkodi K (2009) Optimization using civilized swarm: solution to economic dispatch with multiple minima. Electr Power Syst Res 79:8–16

    Article  Google Scholar 

  • Seo JH, Im CH, Heo CG (2006) Multimodal function optimization based on particle swarm optimization. IEEE Trans Magn 42(4):1095–1098

    Article  Google Scholar 

  • 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 32:432–448

    Article  Google Scholar 

  • Shelokar PS, Siarry P, Jayaraman VK, Kulkarni BD (2007) Particle swarm and ant colony algorithms hybridized for improved continuous optimization. Appl Math Comput 188:129–142

    MathSciNet  MATH  Google Scholar 

  • 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, 1998

  • 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, 2001

  • Shin Y, Kita E (2014) Search performance improvement of particle swarm optimization by second best particle information. Appl Math Comput 246:346–354

    MathSciNet  MATH  Google Scholar 

  • 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 21:1171–1183

    Article  Google Scholar 

  • Sierra MR, Coello CAC (2005) Improving pso-based multi-objective optimization using crowding, mutation and epsilon-dominance. Lect Notes Comput Sci 3410:505–519

    Article  MATH  Google Scholar 

  • 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 39:3990–4012

    Article  MathSciNet  Google Scholar 

  • 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, 2003

  • 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, 1999

  • 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, 2004

  • Tang Y, Wang Z, Fang J (2011) Feedback learning particle swarm optimization. Appl Soft Comput 11:4713–4725

    Article  Google Scholar 

  • 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 326:1–24

    Article  Google Scholar 

  • 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):8991–9011

    MathSciNet  MATH  Google Scholar 

  • Tatsumi K, Ibuki T, Tanino T (2015) Particle swarm optimization with stochastic selection of perturbation-based chaotic updating system. Appl Math Comput 269:904–929

    MathSciNet  Google Scholar 

  • 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, 2003

  • Trelea IC (2003) The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf Process Lett 85(6):317–325

    Article  MathSciNet  MATH  Google Scholar 

  • 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):496–506

    Article  Google Scholar 

  • van den Bergh F (2001) An analysis of particle swarm optimizers. Ph.D. dissertation, University of Pretoria, Pretoria, South Africa

  • 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, 2002

  • van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evolut Comput 8(3):225–239

    Article  Google Scholar 

  • van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176:937–971

    Article  MathSciNet  MATH  Google Scholar 

  • Vitorino LN, Ribeiro SF, Bastos-Filho CJA (2015) A mechanism based on artificial bee colony to generate diversity in particle swarm optimization. Neurocomputing 148:39–45

    Article  Google Scholar 

  • 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):991–1001

    Article  Google Scholar 

  • Wang W (2012) Research on particle swarm optimization algorithm and its application. Southwest Jiaotong University, Doctor Degree Dissertation, pp 36–37

  • Wang Q, Wang Z, Wang S (2005) A modified particle swarm optimizer using dynamic inertia weight. China Mech Eng 16(11):945–948

    Google Scholar 

  • Wang H, Wu Z, Rahnamayan S, Liu Y, Ventresca M (2011) Enhancing particle swarm optimization using generalized opposition-based learning. Inf Sci 181:4699–4714

    Article  MathSciNet  Google Scholar 

  • Wang H, Sun H, Li C, Rahnamayan S, Pan J (2013) Diversity enhanced particle swarm optimization with neighborhood search. Inf Sci 223:119–135

    Article  MathSciNet  Google Scholar 

  • Wen W, Liu G (2005) Swarm double-tabu search. In: First international conference on intelligent computing, pp 1231–1234, Changsha, China, August 23–26, 2005

  • Wolpert DH, Macready WG (1997) Free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67–82

    Article  Google Scholar 

  • 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, 2002

  • 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, 2004

  • 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, 2005

  • 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, 2006

  • Yang X, Yuan J, Yuan J, Mao H (2007) A modified particle swarm optimizer with dynamic adaptation. Appl Math Comput 189:1205–1213

    MathSciNet  MATH  Google Scholar 

  • 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 29:386–394

    Article  Google Scholar 

  • 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, 2003

  • 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, 2004

  • 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):675–680

    Google Scholar 

  • 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 270:74–89

    MathSciNet  Google Scholar 

  • 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, 2005

  • 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 149:573–584

    Article  Google Scholar 

  • Zhan Z, Zhang J, Li Y, Chung HH (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybernet Part B Cybernet 39(6):1362–1381

    Article  Google Scholar 

  • Zhan Z, Zhang J, Li Y, Shi Y (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evolut Comput 15(6):832–847

  • 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, 2003

  • 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 99:18–29

    Article  Google Scholar 

  • 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 28:138–149

    Article  Google Scholar 

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Acknowledgements

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

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  1. School of Electrical Engineering, Zhengzhou University, Zhengzhou, 450001, Henan, China

    Dongshu Wang & Dapei Tan

  2. Department of Research, The People’s Bank of China, Zhengzhou Central Sub-Branch, Zhengzhou, China

    Lei Liu

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  1. Dongshu Wang
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Wang, D., Tan, D. & Liu, L. Particle swarm optimization algorithm: an overview. Soft Comput 22, 387–408 (2018). https://doi.org/10.1007/s00500-016-2474-6

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