Skip to main content
SpringerLink
Log in

A supervised particle swarm algorithm for real-parameter optimization

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Particle swarm optimization (PSO) is a heuristics method based on a homogeneous population with identical search behavior. The simple homogeneous search is not always optimal. Recently, heterogeneous PSO (HPSO) search mechanisms have been developed to allow each particle to have different update rules for its position and velocity. However, in existing HPSOs, there are no supervisors to guide the particles to execute different search tasks. Differently, this paper investigates a new HPSO named SuPSO with a supervisor to allocate different tasks for each particle. In SuPSO the particles are separated into three groups by support vector machine (SVM): exploitation particles (EPs), diverse particles (DPs), and support particles (SPs). The supervisor enables the particle swarm to perform different tasks consisting of local search by EPs, global search by DPs, and linkage by SPs. The proposed SuPSO also employs a swarm migration mechanism, which, together with the DPs, enhances multi-modal optimization. The SuPSO algorithm was compared with other ten algorithms over twenty-eight benchmark functions (CEC2013). Based on the statistical analysis, we showed that SuPSO is statistically different from other ten algorithms with p-value less than 8×10−3 and able to achieve good performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the IEEE Conference, IEEE Service Center, Perth, Australia, pp 1942–1948

  2. Shi Y, Eberhart RC (1998) A modified particle swarm optimizer

  3. 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 

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

    Article  Google Scholar 

  5. 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 

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

    Article  Google Scholar 

  7. Suganthan P (1999) Particle swarm optimiser with neighbourhood operator. In: Proceedings of the 1999 Congress on Evolutionary Computation, vol 3, pp 1958–1962

  8. Peram T, Veeramachaneni K, Mohan CK (2003) Fitness-distance-ratio based particle swarm optimization. In: Proceeding in Swarm Intelligence Symposium, pp 174–181

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

    Article  Google Scholar 

  10. Parsopoulos KE, Vrahatis MN (2004) UPSO: a unified particle swarm scheme. In: Lecture series on Computer and Computational Sciences, vol 1, pp 868–873

  11. 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 

  12. Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: IEEE Symposium on Swarm Intelligence, pp 120–127

  13. Montes de Oca M, Pena J, Stutzle T, Pinciroli C, Dorigo M (2009) Heterogeneous particle swarm optimizers. In: IEEE Congress on Evolutionary Computation, pp 698–705

  14. Engelbrecht AP (2010) Heterogeneous particle swarm optimization. In: Swarm Intelligence, Lecture Notes in Computer Science, vol 6234, Springer Berlin Heidelberg, pp 191–202

  15. Engelbrecht AP (2011) Scalability of a heterogeneous particle swarm optimizer. In: IEEE Symposium on Swarm Intelligence, pp 1–8

  16. Leonard B, Engelbrecht A, van Wyk A (2011) Heterogeneous particle swarms in dynamic environments. In: IEEE Symposium on Swarm Intelligence, pp 1–8

  17. Cheung N J, Ding X-M, Shen H-B (2014) OptiFel: a Convergent Heterogeneous Particle Swarm Optimization Algorithm for Takagi-Sugeno Fuzzy Modeling. IEEE Trans Fuzzy Syst 22(4):919–933

    Article  Google Scholar 

  18. Cheung NJ, Xu Z-K, Ding X-M, Shen H-B (2015) Modeling nonlinear dynamic biological systems with human-readable fuzzy rules optimized by convergent heterogeneous particle swarm

  19. de Oca M, Stutzle T, Van den Enden K, Dorigo M (2011) Incremental social learning in particle swarms. IEEE Trans Syst Man Cybern B Cybern 41(2):368–384

    Article  Google Scholar 

  20. Koh BI, George AD, Haftka RT, Fregly BJ (2006) Parallel asynchronous particle swarm optimization. Int J Numer Methods Eng 67(4):578–595

    Article  MATH  Google Scholar 

  21. Schutte JF, Haftka RT, Fregly BJ (2007) Improved global convergence probability using multiple independent optimizations. Int J Numer Methods Eng 71(6):678–702

    Article  MATH  Google Scholar 

  22. Parpinelli RS, Teodoro FR, Lopes HS (2012) A comparison of swarm intelligence algorithms for structural engineering optimization. Int J Numer Methods Eng 91(6):666–684

    Article  MATH  Google Scholar 

  23. Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Data Mining Knowledge Discov 2:41–47

    Article  Google Scholar 

  24. Aytug H, Sayin S (2012) Exploring the trade-off between generalization and empirical errors in a one-norm SVM. Eur J Oper Res 218(3):667–675

    Article  MATH  Google Scholar 

  25. Natha JS, Shevadeb SK (2006) An efficient clustering scheme using support vector methods. Pattern Recognit 39:1473–1480

    Article  Google Scholar 

  26. Cortes C, Vapnik V (1995) Support vector networks. Mach Learn 20:273–297

    MATH  Google Scholar 

  27. Paquet U, Engelbrecht A (2003) Training support vector machines with particle swarms. In: Proceedings of the International Joint Conference on Neural Networks, vol 2, pp 1593– 1598

  28. Shen Q, Shi WM, Kong W, Ye BX (2007) A combination of modified particle swarm optimization algorithm and support vector machine for gene selection and tumor classification. Talanta 71(4):1679–1683

    Article  Google Scholar 

  29. Chen X, Han J (2008) A novel classification approach based on support vector machine and adaptive particle swarm optimization algorithm. In: International Symposium on Knowledge Acquisition and Modeling, pp 703–707

  30. Liu Z, Wang C, Yi S (2009) A combination of modified particle swarm optimization algorithm and support vector machine for pattern classification. In: Third International Symposium on Intelligent Information Technology Application, vol 3, pp 126–129

  31. 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 

  32. 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, Tech. rep., Nanyang Technological University

  33. Liang JJ, Qu B-Y, Suganthan PN, Hernández-Díaz Alfredo G (2013) Problem Definitions and Evaluation Criteria for the CEC, 2013 Special Session and Competition on Real-Parameter Optimization, Technical Report 201212, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore, January, 2013

  34. Clerc M (2012) Standard particle swarm optimisation. http://clerc.maurice.free.fr/pso/SPSO_descriptions.pdf

  35. Kennedy J, Mendes R (2002) Population structure and particle swarm performance. In: Proceedings of the 2002 Congress on Evolutionary Computation, vol 2, pp 1671– 1676

  36. Zhao SZ, Suganthan P, Das S (2010) Dynamic multi-swarm particle swarm optimizer with sub-regional harmony search. In: IEEE Congress on Evolutionary Computation (CEC), pp 1–8

  37. Wilke DN, Kok S, Groenwold AA (2007) Comparison of linear and classical velocity update rules in particle swarm optimization: notes on diversity. Int J Numer Methods Eng 70(8):962–984

    Article  MATH  MathSciNet  Google Scholar 

  38. Ursem Rasmus K Diversity-Guided Evolutionary Algorithms (2002) Proceedings of the 7th International Conference on Parallel Problem Solving from Nature, PPSN VII, pp 462–474

  39. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the China Scholarship Council and the Hujiang Foundation of China (C14002).

Author information

Authors and Affiliations

  1. Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Ngaam J. Cheung & Hong-Bin Shen

  2. Key Laboratory of System Control and Information Processing, Ministry of Education of China, 800 Dongchuan Road, Shanghai, 200240, China

    Ngaam J. Cheung & Hong-Bin Shen

  3. School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai, 200093, China

    Xue-Ming Ding

  4. James Franck Institute and Department of Chemistry, The University of Chicago, Chicago, IL, 60637, USA

    Ngaam J. Cheung

Authors
  1. Ngaam J. Cheung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xue-Ming Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong-Bin Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ngaam J. Cheung.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(PDF 3.28 MB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheung, N.J., Ding, XM. & Shen, HB. A supervised particle swarm algorithm for real-parameter optimization. Appl Intell 43, 825–839 (2015). https://doi.org/10.1007/s10489-015-0683-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-015-0683-9

Keywords

Search

Navigation