Hybrid Dynamical Evolutionary Algorithm and Time Complexity Analysis

Abstract:

The dynamical evolutionary algorithm (DEA) is a new evolutionary algorithm based on the theory of statistical mechanics, however, DEA converges slowly and often converge at local optima for some function optimization problems. In this paper, a hybrid dynamical evolutionary algorithm (HDEA) with multi-parent crossover and differential evolution mutation is proposed for accelerating convergence velocity and easily escaping suboptimal solutions. Moreover, the population of HDEA is initialized by chaos. In order to confirm the effectiveness of our algorithm, HDEA is applied to solve the typical numerical function minimization problems. The computational complexity of HDEA is analyzed, and the experimental results show that HDEA outperforms the DEA in the aspect of convergence velocity and precision, even the two algorithms have the similar time complexity.

• Periodical: Applied Mechanics and Materials (Volumes 263-266)
• Pages: 2344-2348
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.263-266.2344
• Online since: December 2012
• Authors: Hui Ying Li, Yi Lai Zhang, Xing Xu
• Keywords: Chaos, Differential Evolution, Dynamical Evolutionary Algorithm, Multi-Parent Crossover, Time Complexity

References

[1] Pan Zhengjun, Kang Lishan and Chen Yu-pin. Evolutionary computation (Tsinghua University Press,Beijing 1998).

[2] Riccardo C, Luigi F, Stefano F:IEEE Transactions on Evolutionary Computation. Vol.7(3)(2003),pp.289-304.

[3] Mori N, Yoshida J, "A Thermo dynamical Selection Rule for the Genetic Algorithm, " Proc. of the second IEEE International Conference on Evolutionary Computation, Perth, WA,USA,Nov 29,1995.

[4] Bernstein Y, Li Xiaodong., "Critical dynamics in evolutionary algorithms, " CEC '03. 2003.

DOI: 10.1109/cec.2003.1299607

[5] Jiao Licheng, Wang Lei:IEEE Transactions on Systems, Man, and Cybernetics—PART A: Systems and Humans.Vol.30(5)(2000),pp.552-561.

DOI: 10.1109/3468.867862

[6] Li Yuanxiang, Zou Xiufen, Kang Lishan:Chinese Journal of Computer and Science Technology.Vol.18(3)(2003),pp.361-368.

[7] Zou Xiufen, Li Yuanxiang, Kang Lishan:Wuhan University Journal of Natural Sciences. Vol.7(2)(2002),pp.157-160.

[8] Guo Tao, Kang Lishan:Wuhan University Journal of Nature Science.Vol.4(4)(1999), pp.409-414

[9] Storn R, Price K. http://www.icsi.berkeley.edu/ftp/pub/techreports/1995/tr-95-012.pdf

[10] R. Caponetto, M. Criscione, et al, "Synthesis of a programmable chaos generator, based on CNN architectures, with applications in chaotic communication," Proc .CNNA '98, London, U.K., Apr. 14–17, 1998.

DOI: 10.1109/cnna.1998.685347

[11] M. Bucolo, R. Caponetto, et al, "How the chua circuit allows to model population dynamics," Proc. NOLTA '98, La Regent, Crans-Montana, Switzerland, Sept. 14–17, 1998.

[12] H. Nozawa:Chaos, Vol. 2(1992), p.377–386.

[13] P. Arena, R. Caponetto: Int. J. Bifurcation and Chaos.Vol.10(5)(2000), p.1115–1125.

[14] G. Manganaro, J. Pineda de Gyvez, "DNA computing based on chaos," Proc. 1997 IEEE International Conference on Evolutionary.  Indianapolis, IN,Apr.13-16, 1997.

DOI: 10.1109/icec.1997.592306

[15] B.Li, W.S. Jiang:Control Theory and Applications.Vol.14(4)(1997), pp.63-615.