[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

The time complexity analysis of a class of gene expression programming

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper studies the time complexity of gene expression programming based on maintaining elitist (ME-GEP). Using the theory of Markov chain and the technique of artificial fitness level, the properties of transition matrices of ME-GEP are analyzed. Based on the properties, the upper and lower bounds of the average time complexity of ME-GEP are obtained. Furthermore, the upper bound is estimated, which is determined by the parameters of ME-GEP algorithm. And the theoretical results acquired in this paper are used to analyze ME-GEP for solving function modeling and clustering problem. At last, a set of experiments are performed on these problems to illustrate the effectiveness of theoretical results. The results show that the upper bound of expected first hitting time can be used to direct the algorithm design of ME-GEP.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Bin JX, Jie TC et al (2005) Mining frequent function set based on gene expression programming. Chin J Comput 128(8):1247–1254

    Google Scholar 

  • Canakci H, Baykasoglu A, Gullu H (2009) Quantitative structure-activity relationships studies of ccr5 inhibitors and toxicity of aromatic compounds using gene expression programming. Eur J Med Chem 18(8):1031–1041

    Google Scholar 

  • Chen Yu, Tang Changjie et al (2007) Clustering without prior knowledge based on gene expression progarmming. Third Int Conf Nat Comput 3:451–455

    Google Scholar 

  • Chen TS, He J et al (2009) A new approach for analyzing average time complexity of population-based evolutionary algorithms on unimodal problems. IEEE Trans Syst Man Cybern B Cybern 39(5):1092–1106

    Article  Google Scholar 

  • Chi Z, Xiao WM, Thomas MT, Peter CN (2003) Evolving accurate and compact classification rules with gene expression programming. IEEE Trans Evol Comput 7(6):519–531

    Article  Google Scholar 

  • Ding LX, Yu JH (2005) Some theoretical results about the computation time of evolutionary algorithms. In: Proceedings of the 7th annual conference on genetic and evolutionary computation. ACM, Washington, DC, USA, pp 1409–1415

  • Droste S, Jansen T, Wegener I (2002) On the analysis of the (1 + 1) evolutionary algorithms. Theor Comput Sci 276(1–2):51–81

    Article  MATH  MathSciNet  Google Scholar 

  • Du X, Ding LX (2010) About the convergence rates of a class of gene expression programming. Sci China Inform Sci 53(4):715–728

    Article  MathSciNet  Google Scholar 

  • Du X, Ding LX et al (2009) Convergence analysis of gene expression programming based on maintaining elitist. In: Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation, vol 6, pp 823–826

  • Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst 12(2):87–129

    Google Scholar 

  • Garnier J, Kallel L, Schoenauer M (1999) Rigorous hitting times for binary mutations. Evol Comput 7(2):173–203

  • Happ E, Daniel J, Christian K, Frank N (2008) Rigorous analyses of fitness-proportional selection for optimizing linear functions. In: Proceedings of the 10th annual conference on genetic and evolutionary computation. ACM, Atlanta, Georgia, USA, pp 953–960

  • He J, Kang LS (1999) On the convergence rates of genetic algorithms. Theor Comput Sci 229(1–2):23–39

    Article  MATH  MathSciNet  Google Scholar 

  • He J, Yao X (2002) From an individual to a population: an analysis of the first hitting time of population-based evolutionary algorithms. IEEE Trans Evol Comput 6(5):495–511

    Article  Google Scholar 

  • He J, Yao X (2003) Towards an analytic framework for analyzing the computation time of evolutionary algorithms. Artif Intell 145(1–2):59–97

    Article  MATH  MathSciNet  Google Scholar 

  • He J, Yao X (2004) A study of drift analysis of estimating computation time of evolutionary algorithms. Nat Comput 3(1):21–35

  • Iosifescu M (1980) Finite Markov processes and their application. Wiley, Chichester

    Google Scholar 

  • Karakasis V, Stafylopatis A (2008) Efficient evolution of accurate classification rules using a combination of gene expression programming and clonal selection. IEEE Tran Evol Comput 12(6):662–678

    Article  Google Scholar 

  • Lehre PK, Yao X (2012) On the impact of mutation-selection balance on the runtime of evolutionary algorithms. IEEE Trans Evol Comput 16(2):225–241

    Article  Google Scholar 

  • Lopes HS, Weinert WR (2004) A gene expression programming system for time series modeling. In: Proceedings of XXV Iberian Latin American Congress on Computational Methods in Engineering, vol 11. CILAMCE, Recife, pp 10–12

  • Oliveto PS, Witt C, (2008) Simplified drift analysis for proving lower bounds in evolutionary computation. In: Proceeding of the 10th International Conference on Parallel Problem Solving from Nature, pp 82–91

  • Oliveto PS, He J, Yao X (2007) Computational complexity analysis of evolutionary algorithms for combinatorial optimization: a decade of results. J Autom Comput 4(3):281–293

    Article  Google Scholar 

  • Peng J, Jie TC et al (2005) M-GEP: a new evolution algorithm based on multi-layer chromosomes gene expression programming. Chin J Comput 9(28):1459–1466

    Google Scholar 

  • Rudolph G (1994) Convergence analysis of canonical genetic algorithm. IEEE Trans Neural Netw 5:96–101

    Article  Google Scholar 

  • Rudolph G (1996) How mutation and selection solve long path problems in polynomial expected time. Evol Comput 4(2):194–205

    Article  Google Scholar 

  • Shi W, Zhang X, Shen Q (2010) Quantitative structure-activity relationships studies of ccr5 inhibitors and toxicity of aromatic compounds using gene expression programming. IEEE Trans Evol Comput 45(1):49–54

    Google Scholar 

  • Smith MJ, Szathmry E (1995) The major transitions in evolution. Oxford University Press, Oxford

    Google Scholar 

  • Teodorescu L (2004) Gene expression programming approach to event selection in high energy physics. IEEE Trans Nuclear Sci 53(6):2221–2227

    Google Scholar 

  • Teodorescu L, Sherwood D (2008) High energy physics event selection with gene expression programming. Comput Phys Commun 178(6):409–419

    Article  Google Scholar 

  • Wegener I, Witt C (2005) On the analysis of a simple evolutionary algorithm on quadratic pseudo-boolean function. J Discrete Algorithm 3(1):61–78

    Article  MATH  MathSciNet  Google Scholar 

  • Xin D, Qiao LY, Tong XD, Shan KL (2006) A new algorithm of automatic programming: GEDGEP. In: The 6th International Conference on Simulated Evolution and Learning, vol 10. Springer, Hefei, pp 292–301

  • Yu Y, Zhou ZH (2008) A new approach to estimating the expected first hitting time of evolutionary algorithms. Artif Intell 172(15):1809–1832

    Article  MATH  MathSciNet  Google Scholar 

  • Yuan CA et al (2004) Function mining based on gene expression programming-convergence analysis and remnant-guided evolution algorithm. J Sichun Univ 36(6):100–105

    Google Scholar 

  • Yuan CA et al (2006) Convergence of genetic regression in data mining based on gene expression programming and optimized solution. Int J Comput Appl 28(4):359–366

    Google Scholar 

  • Zhou Chi, Xiao W, Tirpak TM, Nelsom PC (2003) Evolving accurate and compact classification rules with gene expression programming. IEEE Trans Evol Comput 7(6):519–531

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61305079, 61305086, 61203306), the project of preeminent youth fund of Fujian province (JA12471), outstanding young teacher training fund of Fujian Normal University (No. fjsdjk2012083), the open fund of State Key Laboratory of Software Engineering (No. SKLSE2012-09-28). Finally, we thank Prof. Jinghu Yu for discussing some issues about this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xin Du.

Additional information

Communicated by U. Fiore.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, X., Ni, Y., Xie, D. et al. The time complexity analysis of a class of gene expression programming. Soft Comput 19, 1611–1625 (2015). https://doi.org/10.1007/s00500-014-1551-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-014-1551-y

Keywords

Navigation