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About the convergence rates of a class of gene expression programming

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Abstract

This paper studies the convergence rates of gene expression programming based on maintaining elitist (ME-GEP) by means of Markov chain and spectrum analysis. We obtain the following results: (1) ME-GEP algorithm converges to the global optimum in probability. (2) The convergence rates of ME-GEP algorithm depend on the revised spectral radius of transition matrix of Markov chain corresponding to the algorithm. (3) The upper bounds of revised spectral radius are estimated, which are determined by the parameters of ME-GEP algorithm. (4) As an application of the theoretical results acquired in the paper, the convergence rates of ME-GEP for the polynomial function modeling problem are also analyzed, which verifies the relations between the convergence rates and the algorithm parameters.

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References

  1. Ferreira C. Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence. 2nd ed. Berlin: Springer-Verlag, 2006

    MATH  Google Scholar 

  2. Peng J, Tang C J, Li C, et al. M-GEP: A new evolution algorithm based on multi-layer chromosomes gene expression programming (in Chinese). Chinese J Comput, 2005, 9: 1459–1466

    Google Scholar 

  3. Du X, Li Y Q, Xie D T, et al. A new algorithm of automatic programming: GEDGEP. In: The 6th International Conference on Simulated Evolution and Learning, Hefei, 2006. 292–301

  4. Zuo J, Tang C J, Li C, et al. Time series prediction based on gene expression programming (in Chinese). Int Confer Web Inf Age, 2004, 31: 55–64

    Google Scholar 

  5. Zhou C, Xiao W M, Tirpak T M, et al. Evolving accurate and compact classification rules with gene expression programming. IEEE Trans Evolut Comput, 2003, 7: 519–531

    Article  Google Scholar 

  6. Jia X B, Tang C J, Zuo J, et al. Mining frequent function set based on gene expression programming (in Chinese). Chinese J Comput, 2005, 28: 1247–1254

    Google Scholar 

  7. Suzuki J. A Markov chain analysis on simple genetic algorithms. IEEE Trans Syst Man Cyber, 1995, 25: 655–659

    Article  Google Scholar 

  8. Schmitt F, Rothlauf F. On the importance of the second largest eigenvalue on the convergence rate of genetic algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference. Sanfrancisco: ACM, 2001. 559–564

    Google Scholar 

  9. He J, Kang L S. On the convergence rates of genetic algorithms. Theor Comput Sci, 1999, 229: 23–39

    Article  MATH  MathSciNet  Google Scholar 

  10. He J, Yu X H. Conditions for the convergence of evolutionary algorithms. J Syst Architect, 2001, 47: 601–612

    Article  Google Scholar 

  11. Yu Y, Zhou Z H. A new approach to estimating the expected first hitting time of evolutionary algorithms. Artif Intell, 2008, 172: 1809–1832

    Article  MATH  MathSciNet  Google Scholar 

  12. He J, Yao X. Drift analysis and average time complexity of evolutionary algorithms. Artif Intell, 2001, 127: 57–85

    Article  MATH  MathSciNet  Google Scholar 

  13. He J, Yao X. A study of drift analysis of estimating computation time of evolutionary algorithms. Nat Comput, 2004, 3: 21–35

    Article  MATH  MathSciNet  Google Scholar 

  14. Oliveto P S, Witt C. Simplified drift analysis for proving lower bounds in evolutionary computation. In: Proceeding of the 10th International Conference on Parallel Problem Solving from Nature. Berlin: Springer-Verlag, 2008. 82–91

    Chapter  Google Scholar 

  15. Yuan C A, Tang C J, Zuo J, et al. Function mining based on gene expression programming-convergence analysis and remnant-guided evolution algorithm (in Chinese). J Sichun Univ, 2004 36: 100–105

    MathSciNet  Google Scholar 

  16. Yuan C A, Tang C J, Wen Y, et al. Convergency of genetic regression in data mining based on gene expression programming and optimized solution. Int J Comput Appl, 2006, 28: 359–366

    Google Scholar 

  17. Mitchell M. An Introduction to Genetic algorithms. Cambridge: MA MIT Press, 1998

    MATH  Google Scholar 

  18. Koza J R. Genetic Programming: On the Programming of Computers by Means of Nature Selection. Cambridge: MA MIT Press, 1992

    Google Scholar 

  19. Rudolph G. Convergence analysis of canonical genetic algorithms. IEEE Trans Neural Networ, 1994, 5: 96–101

    Article  Google Scholar 

  20. Iosifescu M. Finite Markov Processes and Their Application. Chichester: Wiley, 1980

    Google Scholar 

  21. Horn R A, Johnson C R. Matrix Analysis. Beijing: Posts and Telecom Press, 2005

    Google Scholar 

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Authors and Affiliations

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

    Xin Du & LiXin Ding

  2. Department of Information Engineering, Shijiazhuang University of Economics, Shijiazhuang, 050031, China

    Xin Du

Authors
  1. Xin Du
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  2. LiXin Ding
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Correspondence to Xin Du.

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Du, X., Ding, L. About the convergence rates of a class of gene expression programming. Sci. China Inf. Sci. 53, 715–728 (2010). https://doi.org/10.1007/s11432-010-0041-9

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  • DOI: https://doi.org/10.1007/s11432-010-0041-9

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