Skip to main content
SpringerLink
Log in

A new fuzzy adaptive simulated annealing genetic algorithm and its convergence analysis and convergence rate estimation

  • Regular Papers
  • Intelligent and Information Systems
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Due to shortcomings of genetic algorithm that its convergence speed is slow and it is often premature convergence, a new improved genetic algorithm—fuzzy adaptive simulated annealing genetic algorithm (FASAGA) is presented by integrating fuzzy inference, simulated annealing algorithm and adaptive mechanism. The strong Markovian property attributed to the population sequence was deduced by mathematical modeling. Then the convergence in probability of the FASAGA was proved on the condition that the time tended to infinity. Then convergence speed of FASAGA was estimated and some quantitative results were achieved. The simulation results validated the theoretical analysis conclusions. This work is helpful to further analyze and improve optimization performance of FASAGA and other hybrid genetic algorithms.

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

Similar content being viewed by others

References

  1. M. Srinivas, “Adaptive probabilities of crossover and mutation in genetic algorithms,” IEEE Trans. on Systems, Man and Cybernetics, vol. 24, no. 4, pp. 656–667, April 1994.

    Article  Google Scholar 

  2. L. L. Zhu, H. C. Zhang, and Y. Z. Jtng, “Application of fuzzy adaptive genetic algorithm in multi-sensor multitarget tracking,” Information and Control, vol. 32, no. 7, pp. 711–715, July 2003.

    Google Scholar 

  3. F. Herrera, M. Lozano, and J. L. Verdegay, “Fuzzy connectives based crossover operators to model genetic algorithms population diversity,” Fuzzy Sets and Systems, vol. 92, no. 1, pp. 21–30, November 1997.

    Article  Google Scholar 

  4. Y. Yun and M. Gen, “Performance analysis of adaptive genetic algorithms with fuzzy logic and heuristics,” Fuzzy Optimization and Decision Making, vol. 2, no. 2, pp. 161–175, February 2003.

    Article  MathSciNet  Google Scholar 

  5. M. Kaya, “The effects of two new crossover operators on genetic algorithm performance,” Applied Soft Computing, vol. 11, no. 1, pp. 881–890, January 2011.

    Article  Google Scholar 

  6. O. B. Augusto, S. Rabeau, Ph. Depince, and F. Bennis, “Multi-objective genetic algorithms: A way to improve the convergence rate,” Engineering Applications of Artificial Intelligence, vol. 19, no. 5, pp. 501–510, August 2006.

    Article  Google Scholar 

  7. K. C. Sarma and H. Adeli, “Fuzzy genetic algorithm for optimization of steel structures,” Journal of Structural Engineering, vol. 126, no. 5, pp. 596–614, May 2000.

    Article  Google Scholar 

  8. G. C. Liao, “Application of a fuzzy neural network combined with a chaos genetic algorithm and simulated annealing to short-term load forecasting,” IEEE Trans. on Evolutionary Computation, vol. 10, no. 3, pp. 330–340, June 2006.

    Article  Google Scholar 

  9. C. F. Juang, “A hybrid of genetic algorithm and particle swarm optimization for recurrent network design,” IEEE Trans. on Systems, Man and Cybernetics—Part B: Cybernetics, vol. 34, no. 2, pp. 997–1006, April 2004.

    Article  Google Scholar 

  10. L. C. Jiao and L. Wang, “A novel genetic algorithm based on immunity,” IEEE Trans. on Systems, Man and Cybernetics—Part A: Systems and Humans, vol. 30, no. 5, pp. 552–561, September 2000.

    Article  Google Scholar 

  11. X. P. Luo and W. Wei, “A new immune genetic algorithm and its application in redundant manipulator path planning,” Journal of Robotic Systems, vol. 21, no. 3, pp. 141–151, March 2004.

    Article  Google Scholar 

  12. Y. C. Chiu, L. C. Chang, and F. J. Chang, “Using a hybrid genetic algorithm-simulated annealing algorithm for fuzzy programming of reservoir operation,” Hydrol. Process, vol. 21, no. 3, pp. 3162–3172, November 2007.

    Article  MathSciNet  Google Scholar 

  13. J. M. Xie, X. F. Xu, B. Chen, Y. P. Chen, and W. Ai, “Optimized scheduling of electrical vehicle network based on genetic simulated,” China Mechanical Engineering, vol. 8, no. 14, pp. 1697–1700, July 2007.

    Google Scholar 

  14. X. Wang, A. G. Jiang, and S. Wang, “Optimal designs of wireless sensor network by adapted GASA,” Control Theory & Applications, vol. 23, no. 4, pp. 593–596, April 2006.

    MATH  Google Scholar 

  15. K. P. Wong and S. Y. W. Wong, “Combined genetic algorithm/simulated annealing/fuzzy set approach to short-term generation scheduling with take-or-pay fuel contract,” IEEE Trans. on Power System, vol. 11, no. 1, pp. 128–136, February 1996.

    Article  Google Scholar 

  16. W. X. Zhang and Y. Leung, Mathematical Foundation of Genetic Algorithms, The Xi’an Jiaotong University Pres, Xi’an, China. 2000.

    Google Scholar 

  17. D. Reynolds and J. Gomatam, “Theoretical bounds for genetic algorithms,” Proc. of International Conference on Artificial Neural Networks and Genetic Algorithms, Ales, France. pp. 148–151, 1995.

    Google Scholar 

  18. H. Peng and X. H. Wang, “The convergence rate estimation of genetic algorithm with elitist,” Chinese Science Bulletin, vol. 42, no. 2, pp. 144–147, February 1997.

    MathSciNet  Google Scholar 

  19. L. He, K. J. Wang, G. B. Li, and H. Z. Jin, “The convergence rate estimation of genetic algorithm,” Systems Engineering-Theory Methodology Application, vol. 8, no. 3, pp. 22–26, March 1999.

    Google Scholar 

  20. W. Z. Yang, D. L. Li, and L. Zhu, “An improved genetic algorithm for optimal feature subset selection from multi-character feature set,” Expert Systems with Applications, vol. 38, no. 3, pp. 2733–2740, March 2011.

    Article  Google Scholar 

  21. G. Rudoph, “Convergence analysis of canonical genetic algorithms,” IEEE Trans. on Neural Networks, vol. 5, no. 1, pp. 96–101, January 1994.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, P. R. China

    Yonggang Peng & Wei Wei

  2. Zhejiang University City College, Hangzhou, 310015, P. R. China

    Xiaoping Luo

Authors
  1. Yonggang Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoping Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonggang Peng.

Additional information

Recommended by Associate Editor Sungshin Kim under the direction of Editor Zengqi Sun.

This work is supported by the NSFC (61203299), the Natural Science Foundation of Zhejiang province, China (Y1110135, LY12F03018), the Fundamental Research Funds for the Central Universities (2013QNA4021), the Zhejiang Province “Qiangjiang” Talents Program of China (2013R10047) and National 863 Projects of China (2014AA052001).

Yonggang Peng received his Ph.D. degree in Control Theory and Control Engineering from Zhejiang University in 2008 and now he is an associate professor in Zhejiang University. His research interests include intelligent control, evolutionary optimization, and smart grid.

Xiaoping Luo received his Ph.D. degree in Control Theory and Control Engineering from Zhejiang University in 2008. His research interests include evolutionary optimization, and intelligent control.

Wei Wei received his Ph.D. degree in Control Theory and Control Engineering from Zhejiang University in 1994 and now he is a professor in Zhejiang University. His research interests include intelligent control, robot, and smart grid.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, Y., Luo, X. & Wei, W. A new fuzzy adaptive simulated annealing genetic algorithm and its convergence analysis and convergence rate estimation. Int. J. Control Autom. Syst. 12, 670–679 (2014). https://doi.org/10.1007/s12555-011-0022-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-011-0022-9

Keywords

Search

Navigation