Skip to main content
Log in

Hybrid PSO6 for hard continuous optimization

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In our previous works, we empirically showed that a number of \(6_{\pm 2}\) informants may endow particle swarm optimization (PSO) with an optimized learning procedure in comparison with other combinations of informants. In this way, the new version PSO6, that evolves new particles from six informants (neighbors), performs more accurately than other existing versions of PSO and is able to generate good particles for a longer time. Despite this advantage, PSO6 may show certain attraction to local basins derived from its moderate performance on non-separable complex problems (typically observed in PSO versions). In this paper, we incorporate a local search procedure to the PSO6 with the aim of correcting this disadvantage. We compare the performance of our proposal (PSO6-Mtsls) on a set of 40 benchmark functions against that of other PSO versions, as well as against the best recent proposals in the current state of the art (with and without local search). The results support our conjecture that the (quasi)-optimally informed PSO, hybridized with local search mechanisms, reaches a high rate of success on a large number of complex (non-separable) continuous optimization functions.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. MALLBA Library, Directory Mallba/rep/PSO/soco2010

    http://neo.lcc.uma.es/mallba/easy-mallba/html/mallba.html.

  2. The complete information about featured algorithms in SOCO’10 is available in http://sci2s.ugr.es/EAMHCO/.

References

  • Alba E, Luque G, García-Nieto J, Ordoñez G, Leguizamón G (2007) MALLBA: a software library to design efficient optimisation algorithms. Int J Innovative Comput Appl (IJICA) 1(1):74–85

    Article  Google Scholar 

  • Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. IEEE Congr Evol Comput 2:1769–1776

    Google Scholar 

  • Chen J, Qin Z, Liu Y, Lu J (2005) Particle swarm optimization with local search. In: Neural Networks and Brain, 2005. ICNN B ’05. International Conference on, vol 1, pp 481–484

  • 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

  • Das S, Koduru P, Gui M, Cochran M, Wareing A, Welch SM, Babin BR (2006) Adding local search to particle swarm optimization. In: IEEE Congress on Evolutionary Computation, CEC 2006, pp 428–433

  • dos Santos Coelho L, Mariani VC (2006) Particle swarm optimization with quasi-newton local search for solving economic dispatch problem. In: IEEE International Conference on Systems, Man and Cybernetics, SMC 2006, vol 4, pp 3109–3113

  • Eberhart R, Shi Y (2000) Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the IEEE Congress on Evolutionary Computation CEC’00., vol 1, La Jolla, pp 84–88

  • El Dor A, Clerc M, Siarry P (2012) A multi-swarm PSO using charged particles in a partitioned search space for continuous optimization. Comput Optim Appl 53(1):271–295

    Article  MATH  MathSciNet  Google Scholar 

  • García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005. J Heuristics 15(6):617–644

    Article  MATH  Google Scholar 

  • García-Nieto J, Alba E (2011) Empirical computation of the quasi-optimal number of informants in particle swarm optimization. In: Proceedings of the 13th annual conference on Genetic and evolutionary computation, GECCO ’11. ACM, New York, pp 147–154

  • García-Nieto J, Alba E (2012) Why six informants is optimal in PSO. In: Proceedings of the fourteenth international conference on Genetic and evolutionary computation conference, GECCO ’12. ACM, New York, pp 25–32

  • Herrera F, Lozano M (2009) Workshop for evolutionary algorithms and other metaheuristics for continuous optimization problems: a scalability test. Technical report, SCI2S, University of Granada, Pisa

  • Herrera F, Lozano M, Molina D (2010) Test suite for the special issue of soft computing on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems. Technical report, SCI2S, University of Granada, Spain

  • Kennedy J, Eberhart RC (2001) Swarm intelligence. Morgan Kaufmann Pub, San Francisco

    Google Scholar 

  • Kennedy J, Mendes R (2002) Population structure and particle swarm performance. In: Proceedings of the Congress of Evolutionary Computation CEC’02, vol 2. IEEE Computer Society, Washington, DC, pp 1671–1676

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

    Article  Google Scholar 

  • Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer with local search. In: The IEEE Congress on Evolutionary Computation, CEC 2005, vol 1, pp 522–528

  • Liao T, Montes de Oca MA, Aydin D, Stützle T, Dorigo M (2011) An incremental ant colony algorithm with local search for continuous optimization. In: Proceedings of the 13th annual conference on Genetic and evolutionary computation, GECCO ’11. ACM, New York, pp 125–132

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

  • Mohais AS, Mendes R, Ward C, Posthoff C (2005) Neighborhood re-structuring in particle swarm optimization. In: LNCS 3809. Proceedings of the 18th Australian Joint Conference on Artificial Intelligence. Springer, New York, pp 776–785

  • Monson CK, Seppi KD (2005) Exposing origin-seeking bias in PSO. In: Proceedings of the 2005 conference on Genetic and evolutionary computation, GECCO ’05. ACM, New York, pp 241–248

  • Montes de Oca MA, Aydin D, Stützle T (2011) An incremental particle swarm for large-scale continuous optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms. Soft Comput 15:2233–2255

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Muelas S, La Torre A, Peña J (2009) A memetic differential evolution algorithm for continuous optimization. In: Proceedings of the 2009 Ninth International Conference on Intelligent Systems Design and Applications, ISDA ’09. IEEE Computer Society, Washington, DC, pp 1080–1084

  • Muelas S, Peña J, La Torre A, Robles V (2010) A new initialization procedure for the distributed estimation of distribution algorithms. Soft Comput 15(4):713–720

    Article  Google Scholar 

  • Müller CL, Baumgartner B, Sbalzarini IF (2009) Particle swarm cma evolution strategy for the optimization of multi-funnel landscapes. In: Proceedings of the Eleventh conference on Congress on Evolutionary Computation, CEC’09. IEEE Press, Piscataway, pp 2685–2692

  • Powell MJD (1964) An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput J 7(2):155–162

  • PSO-Central-Group (2011) Standard PSO 2006, 2007, and 2011. Technical Report [online] http://www.particleswarm.info/. Particle Swarm Central, Jan 2011

  • Qu B, Liang J, Suganthan P (2012) Niching particle swarm optimization with local search for multi-modal optimization. Inform Sci 197:131–143

    Article  Google Scholar 

  • Sheskin DJ (2007) Handbook of parametric and nonparametric statistical procedures. Chapman & Hall/CRC, New York

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC’05 special session on real-parameter optimization. Technical Report KanGAL Report 2005005, Nanyang Technological University, Singapore and Kanpur, India

  • Sutton AM, Whitley D, Lunacek M, Howe A (2006) PSO and multi-funnel landscapes: how cooperation might limit exploration. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation, GECCO ’06. ACM, pp 75–82

  • Tang K, Yao X, Suganthan PN, MacNish C, Chen YP, Chen CM, Yang Z (2007) Benchmark functions for the CEC’08 special session and competition on large scale global optimization. Technical report, Nature Inspired Computation and Applications Laboratory, USTC, China, November

  • Thain D, Tannenbaum T, Livny M (2005) Distributed computing in practice: the condor experience. Concurr Pract Exp 17(2–4):323–356

    Article  Google Scholar 

  • Tseng L, Chun C (2008) Multiple trajectory search for large scale global optimization. In: IEEE Congress on Evolutionary Computation, CEC’2008. IEEE Press, pp 3052–3059

  • Tseng L, Chen C (2009) Multiple trajectory search for unconstrained/constrained multi-objective optimization. In: Proceedings of the Eleventh conference on Congress on Evolutionary Computation, CEC’09. IEEE Press, Piscataway, pp 1951–1958

Download references

Acknowledgments

Authors acknowledge funds from the Spanish Ministry of Economy and Competitiveness (MEC) and FEDER under contract TIN2011-28194 (RoadMe project http://roadme.lcc.uma.es). It is also partially founded by project number 8.06/5.47.4142 in collaboration with the VSB-Technical University of Ostrava.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to José García-Nieto.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

García-Nieto, J., Alba, E. Hybrid PSO6 for hard continuous optimization. Soft Comput 19, 1843–1861 (2015). https://doi.org/10.1007/s00500-014-1368-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-014-1368-8

Keywords

Navigation