Skip to main content
SpringerLink
Log in

An Analysis About the Asymptotic Convergence of Evolutionary Algorithms

  • Conference paper
Computational Intelligence and Security (CIS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4456))

Included in the following conference series:

  • 956 Accesses

Abstract

This paper discusses the asymptotic convergence of evolutionary algorithms based on finite search space by using the properties of Markov chains and Perron-Frobenius Theorem. First, some convergence results of general square matrices are given. Then, some useful properties of homogeneous Markov chains with finite states are investigated. Finally, the geometric convergence rates of the transition operators, which is determined by the revised spectral of the corresponding transition matrix of a Markov chain associated with the EA considered here, are estimated by combining the acquired results in this paper.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agapie, A.: Theoretical analysis of mutation-adaptive evolutionary algorithms. Evolutionary Computation 9, 127–146 (2001)

    Article  Google Scholar 

  2. Cerf, R.: Asympototic Convergence of Genetic Algorithms. Advances in Applied Probablity 30, 521–550 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. He, J., Kang, L.: On the convergence rate of genetic algorithms. Theoretical Computer Science 229, 23–39 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lozano, J.A., et al.: Genetic algorithms: bridging the convergence gap. Theoretical Computer Science 229, 11–22 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Nix, A.E., Vose, D.E.: Modeling genetic algorithms with Markov chains. Annals of Mathematics and Artificial Intelligence 5, 79–88 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Poli, R., Langdon, M.: Schema theory for genetic programming with one-point crossover and point mutation. Evolutionary Computation 6, 231–252 (1998)

    Article  Google Scholar 

  7. Poli, R.: Exact schema theory for genetic programming variable-length genetic algorithms with one-point crossover. Genetic Programming and Evolvable Machines 2, 123–163 (2001)

    Article  MATH  Google Scholar 

  8. Rudolph, G.: Convergence analysis of canonical genetic algorithms. IEEE Transactions on Neural Networks 5, 96–101 (1994)

    Article  Google Scholar 

  9. Rudolph, G.: Convergence Properties of Evolutionary Algorithms. Verlag Dr. Kovac, Hamburg (1997)

    Google Scholar 

  10. Schmitt, L.M.: Theory of genetic algorithms. Theoretical Computer Science 259, 1–61 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Suzuki, J.: A further result on the Markov chain model of genetic algorithms and its application to a simulated annealing-like strategy. Man and Cybernetics-Part B 28, 95–102 (1998)

    Article  Google Scholar 

  12. Vose, D.: The Simple Genetic Algorithms: Foundations and Theory. MIT Press, Cambridge (1999)

    MATH  Google Scholar 

  13. Steward, G.W.: Introduction to Matrix Computation. Academic Press, New York (1973)

    Google Scholar 

  14. Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability, 3rd edn. Springer-Verlag, New York (1996)

    Google Scholar 

  15. Isoifescu, M.: Finite Markov Processes and Their Applications. Wiley, Chichester (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Lab of Software Engineering, Wuhan University, Wuhan 430072, China

    Lixin Ding

  2. Department of Mathematics, School of Natural Sciences, Wuhan University of Technology, Wuhan 430070, China

    Jinghu Yu

Authors
  1. Lixin Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinghu Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science and Technology , Xidian University, 710071, Xi’an, China

    Yuping Wang

  2. Department of Computer Science , Hong Kong Baptist University, Hong Kong, China

    Yiu-ming Cheung

  3. Faculty of Applied Mathematics , Guangdong University of Technology, 5100006, Guangzhou, China

    Hailin Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ding, L., Yu, J. (2007). An Analysis About the Asymptotic Convergence of Evolutionary Algorithms. In: Wang, Y., Cheung, Ym., Liu, H. (eds) Computational Intelligence and Security. CIS 2006. Lecture Notes in Computer Science(), vol 4456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74377-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74377-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74376-7

  • Online ISBN: 978-3-540-74377-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation