The Expected First Hitting Time of a class of Gene Expression Programming

Du Xin; Ding Lixin

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The Expected First Hitting Time of a class of Gene Expression Programming

Du Xin 1,Ding Lixin 2 * #

1.State Key Laboratory of Software Engineering,Wuhan University

2.State Key Laboratory of Software Engineering,Wuhan University

*Correspondence author

#Submitted by

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Funding: National Natural Science Foundation of China （No.Grant no. 60975050）, Advanced Interdisciplinary Studies Foundation of Wuhan University （No.Grant no. 6081014）, Research Fund for the Doctoral Program of Higher Education（No.Grant no. 20070486081）

Opened online:26 July 2010

Accepted by: none

Citation: Du Xin ,Ding Lixin .The Expected First Hitting Time of a class of Gene Expression Programming[OL]. [26 July 2010] http://en.paper.edu.cn/en_releasepaper/content/4379501

This paper studies the time complexity of gene expression programming based on maintaining elitist (ME-GEP). By using the theory of Markov Chain and the technique of Artificial fitness level, the upper and lower bounds of the expected first hitting time(EFHT) of ME-GEP are obtained. Furthermore, the unknown parameter of the upper bound is estimated, which is determined by the parameters of ME-GEP algorithm. As an application of the theoretical results acquired in the paper, the EFHT of ME-GEP for solving the polynomial function modeling problem are analyzed, which verifies the relations between the EFHT and the parameters of ME-GEP algorithm. Finally, our theoretical result is used in directing the parameter design of ME-GEP algorithm. And the experiments of solving the above polynomial function modeling problem verify the correctness of our theoretical result.

Keywords:GEP;ME-GEP;Expected First Hitting Time;First Hitting Time; Markov chain; Artificial Fitness Level

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