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. © 2014, Springer-Verlag Berlin Heidelberg.
Bibliographical noteThis 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.
- Artificial fitness level
- Average time complexity
- Markov chain