Constricted Particle Swarm Optimization based Algorithm for Global Optimization

 

Gonzalo Nápoles¹, Isel Grau², and Rafael Bello¹

 

¹ Laboratory of Artificial Intelligence, Universidad Central Marta Abreu de Las Villas (UCLV), Santa Clara, Cuba, (e–mail: gnapoles@uclv.edu.cu, rbellop@uclv.edu.cu).

² Laboratory of Bioinformatics, Universidad Central Marta Abreu de Las Villas (UCLV), Santa Clara, Cuba, (e–mail: igrau@uclv.edu.cu).

 

Manuscript received June 20, 2012.
Manuscript accepted for publication July 24, 2012.

 

Abstract

Particle Swarm Optimization (PSO) is a bioinspired meta–heuristic for solving complex global optimization problems. In standard PSO, the particle swarm frequently gets attracted by suboptimal solutions, causing premature convergence of the algorithm and swarm stagnation. Once the particles have been attracted to a local optimum, they continue the search process within a minuscule region of the solution space, and escaping from this local optimum may be difficult. This paper presents a modified variant of constricted PSO that uses random samples in variable neighborhoods for dispersing the swarm whenever a premature convergence (or stagnation) state is detected, offering an escaping alternative from local optima. The performance of the proposed algorithm is discussed and experimental results show its ability to approximate to the global minimum in each of the nine well–known studied benchmark functions.

Key words: Particle Swarm Optimization, Local optima, Global Optimization, Premature Convergence, Random Samples, Variable Neighborhoods.

 

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REFERENCES

[1] J. Kennedy and R. Eberhart, "Particle Swarm Optimization," in Proc. of the 1995 IEEE International Conference on Neural Networks, Australia, 1995, pp. 1942–1948.         [ Links ]

[2] R. Eberhart and J. Kennedy, "A New Optimizer using Particle Swarm Theory," in Proc. of the Sixth International Symposium on Micromachine and Human Science, Japan, 1995, pp. 39–43.         [ Links ]

[3] D. Bratton and J. Kennedy, "Defining a Standard for Particle Swarm Optimization," in Proc. of the 2007 IEEE Swarm Intelligence Symposium, Honolulu, 2007, pp. 120–127.         [ Links ]

[4] V.J. Huang, et al, "Comprehensive learning particle swarm optimizer for solving multiobjective optimization problems," Int. J. of Intelligent Systems, vol. 21, pp. 209–226, 2006.         [ Links ]

[5] J. Kennedy and C.E. Russell, Swarm Intelligence, Morgan Kaufmann Publishers, 2001.         [ Links ]

[6] G. Evers and M.B. Ghalia, "Regrouping Particle Swarm Optimization: A new Global Optimization Algorithm with Improved Performance Consistency Across Benchmarks," in IEEE International Conference on Systems, Man and Cybernetics, San Antonio, 2009, pp. 3901–3908.         [ Links ]

[7] J. Riget and J.S. Vesterstrom, "A diversity–guide particle swarm optimizer – the arPSO", Tech. Rep., 2002.         [ Links ]

[8] M. Pant and T. Radha, "A new Particle Swarm Optimization with quadratic crossover," in International Conference on Advanced Computing and Communications, India, 2007, pp. 81–86.         [ Links ]

[9] M. Pant, T. Radha and V.P. Singh, "A new diversity based Particle Swarm Optimization using Gaussian Mutation," Int. J. of Mathematical Modeling, Simulation and Applications, vol. 1, pp. 47–60, 2007.         [ Links ]

[10] L. Idoumghar, M. Melkemi, R. Schott and M.I. Aouad, "Hybrid PSOSA Type Algorithms for Multimodal Function Optimization and Reducing Energy Consumption in Embedded Systems," Applied Computational Intelligence and Soft Computing, 12 pages, 2011.         [ Links ]

[11] M. Clerc and J. Kennedy, "The particle swarm – explosion, stability, and convergence in a multidimensional complex space," IEEE Trans. Evolutionary Computation, vol. 6, pp. 58–73, 2002.         [ Links ]

[12] Y. Shi and R. Eberhart, "A Modified Particle Swarm Optimizer," in Proc. of the IEEE Congress on Evolutionary Computation, 1998, pp. 69–73.         [ Links ]

[13] F. Van den Bergh, "An Analysis of Particle Swarm Optimizers," PhD thesis, Univ. of Pretoria, South Africa, 2002.         [ Links ]

[14] P. Hansen and N. Mladenović, "Variable neighborhood search: Principles and applications," European Journal of Operations Research, pp. 449–467, 2001.         [ Links ]

[15] P.N. Suganthan, et al., "Problem definition and evaluation criteria for the CEC 2005 special session on real–parameter optimization," Tech. Rep. 2005005, 2005.         [ Links ]

[16] M. Pant, R. Thangaraj and A. Abraham, "Particle swarm based metaheuristic for function optimization and engineering applications," in Proc. of the 7th Computer Information Systems and Industrial Management Applications, Washington, 2008, pp. 84–90.         [ Links ]

[17] H. Wang, et al., "Opposition–based Particle Swarm Algorithm with Cauchy mutation," in Proc. of the IEEE Congress on Evolutionary Computation, 2007, pp. 4750–4756.         [ Links ]

[18] J. Higgins, Introduction to Modern Nonparametric Statistics, Duxbury Press, 2003.         [ Links ]

[19] S. García, A. Fernández, J. Luengo and F. Herrera, "A study of statistical techniques and performance measures for genetics–based machine learning: Accuracy and interpretability," Soft Computing, vol. 13, no. 10, pp. 959–977, 2009.         [ Links ]

[20] S. García, D. Molina, M. Lozano and F. Herrera, "A study on the use of nonparametric tests for analyzing the evolutionary algorithms' behavior: A case study on the CEC'2005 special session on real parameter optimization," J. Heuristics, vol. 15, pp. 617–644, 2009.         [ Links ]

[21] M. Friedman, "The use of ranks to avoid the assumption of normality implicit in the analysis of variance," Journal of the American Statistical Association, vol. 32, pp. 674–701, 1937.         [ Links ]

[22] M. Friedman, "A comparison of alternative tests of significance for the problem of m rankings," Annals of Mathematical Statistics, vol. 11, pp. 86–92, 1940.         [ Links ]

[23] J. Derrac, S. Garcia, D. Molina and F. Herrera, "A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms," Swarm and Evolutionary Computation, vol. 1, pp. 3–18, 2011.         [ Links ]

[24] J.D. Gibbons and S. Chakraborti, "Nonparametric Statistical Inference," 5th ed., Chapman & Hall, 2010.         [ Links ]