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Phasor particle swarm optimization: a simple and efficient variant of PSO

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Abstract

Particle swarm optimizer is a well-known efficient population and control parameter-based algorithm for global optimization of different problems. This paper focuses on a new and primary sample for PSO, which is named phasor particle swarm optimization (PPSO) and is based on modeling the particle control parameters with a phase angle (θ), inspired from phasor theory in the mathematics. This phase angle (θ) converts PSO algorithm to a self-adaptive, trigonometric, balanced, and nonparametric meta-heuristic algorithm. The performance of PPSO is tested on real-parameter optimization problems including unimodal and multimodal standard test functions and traditional benchmark functions. The optimization results show good and efficient performance of PPSO algorithm in real-parameter global optimization, especially for high-dimensional optimization problems compared with other improved PSO algorithms taken from the literature. The phasor model can be used to expand different types of PSO and other algorithms. The source codes of the PPSO algorithms are publicly available at https://github.com/ebrahimakbary/PPSO.

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References

  • Alatas B, Akin E (2008) Rough particle swarm optimization and its applications in data mining. Soft Comput 12(12):1205–1218

    Article  MATH  Google Scholar 

  • Alatas B, Akin E, Ozer AB (2009) Chaos embedded particle swarm optimization algorithms. Chaos Solut Fract 40(4):1715–1734

    Article  MathSciNet  MATH  Google Scholar 

  • Aljarah I, Faris H, Mirjalili S (2018) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22(1):1–15

    Article  Google Scholar 

  • 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 

  • Arumugam MS, Rao M, Chandramohan A (2008) A new and improved version of particle swarm optimization algorithm with global–local best parameters. Knowl Inf Syst 16(3):331–357

    Article  Google Scholar 

  • Bonyadi MR, Michalewicz Z (2016) Analysis of stability, local convergence, and transformation sensitivity of a variant of particle swarm optimization algorithm. IEEE Trans Evol Comput 20(3):370–385

    Article  Google Scholar 

  • Bonyadi MR, Michalewicz Z, Li X (2014) An analysis of the velocity updating rule of the particle swarm optimization algorithm. J Heuristics 20(4):417–452

    Article  Google Scholar 

  • Campana E, Fasano G, Pinto A (2010) Dynamic analysis for the selection of parameters and initial population, in particle swarm optimization. J Glob Optim 48(3):347–397

    Article  MathSciNet  MATH  Google Scholar 

  • Chatterjee A, Siarry P (2004) Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Comput Oper Res 33(3):859–871

    Article  MATH  Google Scholar 

  • Chen DB, Zhao CX (2009) Particle swarm optimization with adaptive population size and its application. Appl Soft Comput 9(1):39–48

    Article  Google Scholar 

  • Chen W-N et al (2013) Particle swarm optimization with an aging leader and challengers. IEEE Trans Evol Comput 17(2):241–258

    Article  Google Scholar 

  • Chen X, Tianfield H, Mei C, Du W, Liu G (2016) Biogeography-based learning particle swarm optimization. Soft Comput 21:7519–7541

    Article  Google Scholar 

  • Cheng R, Jin Yaochu (2015) A social learning particle swarm optimization algorithm for scalable optimization. Inf Sci 291:43–60

    Article  MathSciNet  MATH  Google Scholar 

  • Cleghorn CW, Engelbrecht AP (2014) A generalized theoretical deterministic particle swarm model. Swarm intell 8(1):35–59

    Article  Google Scholar 

  • Clerc M (2010) Beyond standard particle swarm optimisation. Int J Swarm Intell Res (IJSIR) 1(4):46–61

    Article  Google Scholar 

  • Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73

    Article  Google Scholar 

  • Daneshyari M, Yen GG (2011) Cultural-based multiobjective particle swarm optimization. IEEE Trans Syst Man Cybern B Cybern 41(2):553–567

    Article  Google Scholar 

  • de Oca MAM, Stutzle T, Birattari M, Dorigo M (2009) Frankenstein’s PSO: a composite particle swarm optimization algorithm. IEEE Trans Evol Comput 13(5):1120–1132

    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 system. IEEE Trans Evol Comput 12(2):171–195

    Article  Google Scholar 

  • Deyu T, Cai Y, Zhao J, Xue Y (2014) A quantum-behaved particle swarm optimization with memetic algorithm and memory for continuous non-linear large scale problems. Inf Sci 289:162–189

    Article  Google Scholar 

  • Dorigo M, Maniezzo V, Colorni A (1996) The ant system: optimization by a colony of cooperating agents, IEEE Trans. Syst Man Cybern B Cybern 26:29–41

    Article  Google Scholar 

  • Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of 6th international symposium on micromachine and human science, pp 39–43

  • Fang W, Sun J, Chen H, Wu X (2015) A decentralized quantum-inspired particle swarm optimization algorithm with cellular structured population. Inform Sci 330:19–48

    Article  Google Scholar 

  • Gao H, Xu W (2011) A new particle swarm algorithm and its globally convergent modifications. IEEE Trans Cybern 41(5):1334–1351

    Article  Google Scholar 

  • Ghasemi M, Aghaei J, Akbari E, Ghavidel S, Li L (2016) A differential evolution particle swarm optimizer for various types of multi-area economic dispatch problems. Energy 107:182–195. https://doi.org/10.1016/j.energy.2016.04.002

    Article  Google Scholar 

  • Ghasemi M, Aghaei J, Hadipour M (2017) New self-organising hierarchical PSO with jumping time-varying acceleration coefficients. Electron Lett 53:1360–1362. https://doi.org/10.1049/el.2017.2112

    Article  Google Scholar 

  • Gong YJ, Li JJ, Zhou Y, Li Y, Chung HSH, Shi Y, Zhang J (2016) Genetic learning particle swarm optimization. IEEE Trans Cybern 46(10):2277–2290

    Article  Google Scholar 

  • Gulcu S, Kodaz H (2015) A novel parallel multi-swarm algorithm based on comprehensive learning particle swarm optimization. Eng Appl Artif Intell 45:33–45

    Article  Google Scholar 

  • Helwig S, Branke J, Mostaghim S (2013) Experimental analysis of bound handling techniques in particle swarm optimization. IEEE Trans Evol Comput 17(2):259–271

    Article  Google Scholar 

  • Ho YC, Pepyne DL (2002) Simple explanation of the no-free-lunch theorem and its implications. J Optim Theory Appl 115(3):549–570

    Article  MathSciNet  MATH  Google Scholar 

  • Ho S-Y, Lin H-S, Liauh W-H, Ho S-J (2008) OPSO: orthogonal particle swarm optimization and its application to task assignment problems. IEEE Trans Syst Man Cybern A Syst Hum 38(2):288–298

    Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • Hsieh S, Sun T, Liu C, Tsai S (2009) Efficient population utilization strategy for particle swarm optimizer. IEEE Trans Syst Man Cybern B Cybern 39(2):444–456

    Article  Google Scholar 

  • Islam SM, Das S, Ghosh S, Roy S, Suganthan PN (2012) An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization. IEEE Trans Syst Man Cybern B Cybern 42(2):482–500

    Article  Google Scholar 

  • Jensi R, Jiji GW (2016) An enhanced particle swarm optimization with levy flight for global optimization. Appl Soft Comput 43:248–261

    Article  Google Scholar 

  • Jordehi AR (2014) Particle swarm optimisation for dynamic optimisation problems: a review. Neural Comput Appl 25(7–8):1507–1516

    Article  Google Scholar 

  • Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471

    Article  MathSciNet  MATH  Google Scholar 

  • Kaucic M (2013) A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization. J Glob Optim 55(1):165–188

    Article  MathSciNet  MATH  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, vol 4, pp 1942–1948

  • Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  MathSciNet  MATH  Google Scholar 

  • Krohling RA, dos Santos Coelho L (2006) Coevolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems”. IEEE Trans Syst Man Cybern B Cybern 36(6):1407–1416

    Article  Google Scholar 

  • Kulkarni R, Venayagamoorthy G (2011) Particle swarm optimization in wireless-sensor networks: a brief survey. IEEE Trans Syst Man Cybern C 41(2):262–267

    Article  Google Scholar 

  • Leu M-S, Yeh M-F (2012) Grey particle swarm optimization. Appl Soft Comput 12(9):2985–2996

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Li X, Yao Y (2011) Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans Evol Comput 16(2):1–15

    Google Scholar 

  • Li C-H, Yang S-X, Nguyen TT (2012a) A self-learning particle swarm optimizer for global optimization problems. IEEE Trans Syst Man Cybern B Cybern 42(3):627–646

    Article  Google Scholar 

  • Li Y, Xiang R, Jiao L, Liu R (2012b) An improved cooperative quantumbehaved particle swarm optimization. Soft Comput 16(6):1061–1069

    Article  Google Scholar 

  • Li J, Zhang JQ, Jiang CJ, Zhou MC (2015) Composite particle swarm optimizer with historical memory for function optimization. IEEE Trans Syst Man Cybern 45(10):2350–2363

    Google Scholar 

  • Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Article  Google Scholar 

  • Liang X, Li W, Zhang Y, Zhou M (2015) An adaptive particle swarm optimization method based on clustering. Soft Comput 19(2):431–448

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Liu B, Wang L, Jin Y-H, Tang F, Huang D-X (2005) Improved particle swarm optimization combined with chaos. Chaos Solitons Fract 25(5):1261–1271

    Article  MATH  Google Scholar 

  • Liu Z-H, Zhang J, Zhou S-W, Li X-H, Liu K (2013) Coevolutionary particle swarm optimization using AIS and its application in multiparameter estimation of PMSM. IEEE Trans Cybern 43(6):1921–1935

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Messerschmidt L, Engelbrecht AP (2004) Learning to play games using a PSO-based competitive learning approach. IEEE Trans Evol Comput 8(3):280–288

    Article  Google Scholar 

  • Nickabadi A, Ebadzadeh MM, Safabakhsh R (2011) A novel particle swarm optimization algorithm with adaptive inertia weight. Appl Soft Comput 11(4):3658–3670

    Article  Google Scholar 

  • Omidvar MN, Li X, Mei Y, Yao X (2014) Cooperative co-evolution with differential grouping for large scale optimization. IEEE Trans Evol Comput 18(3):378–393

    Article  Google Scholar 

  • Ouyang HB, Gao LQ, Li S, Kong XY (2017) Improved global-best-guided particle swarm optimization with learning operation for global optimization problems. Appl Soft Comput 52:987–1008

    Article  Google Scholar 

  • Pehlivanoglu YV (2013) A new particle swarm optimization method enhanced with a periodic mutation strategy and neural networks. IEEE Trans Evol Comput 17(3):436–452

    Article  Google Scholar 

  • Qin Q, Cheng S, Zhang Q, Li L, Shi Y (2015) Biomimicry of parasitic behavior in a coevolutionary particle swarm optimization algorithm for global optimization. Appl Soft Comput 32:224–240

    Article  Google Scholar 

  • Qu B, Suganthan P, Das S (2013) A distance-based locally informed particle swarm model for multimodal optimization. IEEE Trans Evol Comput 17(3):387–402

    Article  Google Scholar 

  • Rada-Vilela J, Zhang M, Seah W (2013) A performance study on synchronicity and neighborhood size in particle swarm optimization. Soft Comput 17:1–12

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ren Z-H, Zhang A-M, Wen C-Y, Feng Z-R (2014) A scatter learning particle swarm optimization algorithm for multimodal problems. IEEE Trans Cybern 44(7):1127–1140

    Article  Google Scholar 

  • Shi Y (2014) Developmental swarm intelligence: developmental learning perspective of swarm intelligence algorithms. Int J Swarm Intell Res (IJSIR) 5(1):36–54

    Article  Google Scholar 

  • Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: Proceedings of IEEE world congress on computational intelligence, pp 69–73

  • Shi Y, Liu H, Gao L, Zhang G (2011) Cellular particle swarm optimization. Inf Sci 181(20):4460–4493

    Article  MathSciNet  MATH  Google Scholar 

  • Storn R, Price K (1997) Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Nanyang Technological University, Singapore, technical report

  • Tang KS, Man KF, Kwong S, He Q (1996) Genetic algorithms and their applications. IEEE Signal Process Mag 13(6):22–37

    Article  Google Scholar 

  • Tang Y, Wang Z, Fang J-A (2011) Feedback learning particle swarm optimization. Appl Soft Comput 11(8):4713–4725

    Article  Google Scholar 

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

    Article  Google Scholar 

  • van den Bergh F, Engelbrecht AP (2006) A study of particle optimization particle trajectories. Inf Sci 176(8):937–971

    Article  MathSciNet  MATH  Google Scholar 

  • Wang H, Yang S, Ip WH, Wang D (2012) A memetic particle swarm optimisation algorithm for dynamic multi-modal optimization problems. Int J Syst Sci 43(7):1268–1283

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Wilke D, Kok S, Groenwold A (2007) Comparison of linear and classical velocity update rules in particle swarm optimization: notes on scale and frame invariance. Int J Numer Methods Eng 70(8):985–1008

    Article  MathSciNet  MATH  Google Scholar 

  • Xinchao Z (2010) A perturbed particle swarm algorithm for numerical optimization. Appl Soft Comput 10(1):119–124

    Article  Google Scholar 

  • Zambrano-Bigiarini M, Clerc M, Rojas R (2013) Standard particle swarm optimisa-tion 2011 at EC-2013: a baseline for future PSO improvements. In: 2013 IEEE congress on evolutionary computation (CEC), IEEE, pp 2337–2344

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zhang C, Yi Z (2011) Scale-free fully informed particle swarm optimization algorithm. Inf Sci 181(20):4550–4568

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Electronics and Electrical Engineering, Shiraz University of Technology, Shiraz, Iran

    Mojtaba Ghasemi

  2. Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran

    Ebrahim Akbari

  3. School of Engineering, University of Guelph, Guelph, Canada

    Abolfazl Rahimnejad

  4. Faculty of Electrical and Computer Engineering, University of Birjand, Birjand, Iran

    Seyed Ehsan Razavi

  5. Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, Australia

    Sahand Ghavidel & Li Li

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  1. Mojtaba Ghasemi
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  2. Ebrahim Akbari
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  4. Seyed Ehsan Razavi
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  6. Li Li
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Correspondence to Ebrahim Akbari.

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Ghasemi, M., Akbari, E., Rahimnejad, A. et al. Phasor particle swarm optimization: a simple and efficient variant of PSO. Soft Comput 23, 9701–9718 (2019). https://doi.org/10.1007/s00500-018-3536-8

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