Skip to main content
Log in

Statistical analysis of a multi-objective optimization algorithm based on a model of particles with vorticity behavior

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, a strategy for multi-objective optimization based upon the behavior of a particle swarm with rotational and linear motion is presented. The strategy for multi-objective optimization is based upon the emulation of the linear and circular movements of a swarm (flock). Thus emerges the physical basis for the cognitive model, which in conjunction with exploration–exploitation results in the proposal of a cognitive algorithm, which is tested through several multi-objective optimization functions. The algorithm proposed is compared with standard particle swarm optimization multi-objective via statistical analysis.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Abido M (2008) Multiobjective particle swarm optimization for optimal power flow problem. In: MEPCON 12th international middle-east power system conference, pp 392–396

  • Arriaza A, Fernández M, López A, Muñoz M, Pérez S, Sánchez A (2008) Estadística básica con R y R-Commander. Servicio de Publicaciones de la Universidad de Cádiz

  • Bhagavatula S, Sanjeevi S, Kumar D, Yadav C (2014) Multi-objective indicator based evolutionary algorithm for portfolio optimization. In: IEEE Int Adv Comput Conf (IACC), pp 1206–1210

  • Cabrerizo F, Herrera E, Pedrycz W (2013) A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. Eur J Oper Res 230:624–633

    Article  MathSciNet  MATH  Google Scholar 

  • Cagnina L (2010) Optimización mono y multiobjetivo a través de una heurística de inteligencia colectiva. Tesis de Doctorado, Doctorado en Ciencias de la Computación, Universidad Nacional de San Luis, Argentina

  • Cagnina L, Esquivel S, Coello C (2005) A particle swarm optimizer for multi-objective optimization. J Comput Sci Technol 5(4):204–210

    Google Scholar 

  • Coello C, Van D, Lamont G (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, Berlin

  • Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–3

  • D’Orsogna M, Chuang Y, Bertozzi A, Chayes L (2006) Self-propelled agents with soft-core interactions: patterns, stability, and collapse. Phys Rev Lett 96:104302

  • Ebeling W (2002) Nonequilibrium statistical mechanics of swarms of driven particles. Physica A Stat Mech Appl 314(1–4):92–96

    Article  MathSciNet  MATH  Google Scholar 

  • Espitia H, Sofrony J (2013) Proposal for parameter selection of the vortex particle swarm optimization during the dispersion stage. In: International conference on mechatronics, electronics and automotive engineering (ICMEAE), pp 65–71

  • Espitia H, Sofrony J (2013) Vortex particle swarm optimization. In: IEEE congress on evolutionary computation (CEC), pp 1992-1998

  • 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 Special Session on Real Parameter Optimization. J Heurist 15(6):617–644

    Article  MATH  Google Scholar 

  • Gehlhaar D, Fogel D (1996) Tuning evolutionary programming for conformationally flexible molecular docking. In: Proceedings of evolutionary programming. MIT Press, Cambridge, pp 419–429

  • Heo J, Lee K, Garduno R (2006) Multiobjective control of power plants using particle swarm optimization techniques. IEEE Trans Energy Conv 21(2):552–561

  • Hirano H, Yoshikawa T (2012) A study on two-step search using global-best in PSO for multi-objective optimization problems. In: 6th international conference on soft computing and intelligent systems (SCIS) and 13th international symposium on advanced intelligent systems (ISIS), pp 1894–1897

  • Hochberg Y, Tamhane C (1987) Multiple comparison procedures. Wiley, New York

    Book  MATH  Google Scholar 

  • Idoumghar L, Chérin N, Siarry P, Roche R, Miraoui A (2013) Hybrid ICA-PSO algorithm for continuous optimization. Appl Math Comput 219(24):11149–11170

    MathSciNet  MATH  Google Scholar 

  • Jiang S, Ong Y, Zhang J, Feng L (2014) Consistencies and contradictions of performance metrics in multiobjective optimization. IEEE Trans Cybern 44(12):2391–2404

    Article  Google Scholar 

  • Levine H, Rappel W, Cohen I (2000) Self-organization in systems of self-propelled particles. Phys Rev E 63:017101

  • Man-Fai L, Sin-Chun N, Chi-Chung C, Lui A (2014) A new strategy for finding good local guides in MOPSO. In: IEEE congress on evolutionary computation (CEC), pp 1990–1997

  • Montgomery D (2003) Diseñanálisis de experimentos. Limusa. Wiley, New York

  • Moreno L (2005) Texto y software en diseños experimentales no-paramétricos más importantes. Tesis profesional. Universidad de las Américas Puebla, México

    Google Scholar 

  • Nebro A, Durillo J, Coello C (2013) Analysis of leader selection strategies in a multi-objective particle swarm optimizer. In: IEEE congress on evolutionary computation (CEC), pp 3153–3160

  • Okabe T, Jin Y, Sendhoff B (2003) A critical survey of performance indices for multi-objective optimisation. In: Congress on evolutionary computation CEC ’03, vol 2, pp 878-885

  • Parsopoulos K, Vrahatis M (2008) Multi-objective particles swarm optimization approaches. In: IGI global, multi-objective optimization in computational intelligence: theory and practice, pp 20–42

  • Passino K (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst 22(3):52–67

    Article  MathSciNet  Google Scholar 

  • Reyes M, Coello C (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308

    MathSciNet  Google Scholar 

  • Rubio Á, Zhang Q, Vega M (2015) Multiobjective evolutionary algorithm based on decomposition for 3-objective optimization problems with objectives in different scales. Soft Comput 19(1):157–166

    Article  Google Scholar 

  • Russell E, James K (1995) Particle swarm optimization. IEEE Proc Neural Netw 4:1942–1948

  • Shang R, Jiao L, Ren Y, Li L, Wang L (2014) Quantum immune clonal coevolutionary algorithm for dynamic multiobjective optimization. Soft Comput 18(4):743–756

    Article  MathSciNet  MATH  Google Scholar 

  • Sumpter D (2006) The principles of collective animal behaviour. Philos Trans R Soc B 361, 1465

  • Uchitane T, Hatanaka T (2012) Experimental study for multi-objective PSO with single objective guide selection. In: IEEE congress on evolutionary computation (CEC), pp 1–6

  • Wang H, Yen G (2015) Adaptive multiobjective particle swarm optimization based on parallel cell coordinate system. IEEE Trans Evol Comput 19(1):1–18

    Article  Google Scholar 

  • Wu Y, Jin Y, Liu X (2015) A directed search strategy for evolutionary dynamic multiobjective optimization. Soft Comput 19(11):3221–3235

    Article  Google Scholar 

  • Yan J, Li C, Wang Z, Deng L, Sun D (2007) Diversity metrics in multi-objective optimization: review and perspectives. In: Proceedings of the IEEE international conference on integration technology, pp 553–557

  • Yen G, Wen F (2009) Dynamic multiple swarms in multiobjective particle swarm optimization. IEEE Trans Syst Man Cybern Part A Syst Humans 39(4):890–911

    Article  Google Scholar 

  • Ying G, Lingxi P, Fufang L, Miao L (2014) Multi-objective cloud estimation of distribution particle swarm optimizer using maximum ranking. In: 10th international conference on natural computation (ICNC), pp 321–325

  • Zhang Y, Wu L (2008) Weights optimization of neural network via improved bacterial chemotaxis optimization (BCO) approach. Progr Electromagnet Res PIER 83:185–198

    Article  Google Scholar 

  • Zhi-Hui Z, Jingjing L, Jiannong C, Jun Z (2013) Multiple populations for multiple objectives: a coevolutionary technique for solving multiobjective optimization problems. IEEE Trans Cybernet 43(2):445–463

    Article  Google Scholar 

  • Zitzler E, Thiele L, Laumanns M, Fonseca C, Grunert da Fonseca V (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117–132

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rubén González Crespo.

Ethics declarations

Conflict of interest

The authors declare there is no conflict of interest.

Additional information

Communicated by A. Di Nola.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meza, J., Espitia, H., Montenegro, C. et al. Statistical analysis of a multi-objective optimization algorithm based on a model of particles with vorticity behavior. Soft Comput 20, 3521–3536 (2016). https://doi.org/10.1007/s00500-015-1972-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-015-1972-2

Keywords

Navigation