About the Time Complexity of Evolutionary Algorithms Based on Finite Search Space

Authors:
Lixin Ding;Yingzhou Bi
Affiliations:
State Key Lab of Software Engineering, Wuhan University, Wuhan 430072, China;State Key Lab of Software Engineering, Wuhan University, Wuhan 430072, China and Department of Information Technology, Guangxi Teachers Education University, Nanning 530001, China
Venue:
Computational Intelligence and Security
Year:
2007

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Abstract

We consider some problems about the computation time of evolutionary algorithms in this paper. First, some exact analytic expressions of the mean first hitting times of general evolutionary algorithms in finite search spaces are obtained theoretically by using the properties of Markov chain associated with evolutionary algorithms considered here. Then, by introducing drift analysis and applying Dynkin's Formula, the general upper and lower bounds of the mean first hitting times of evolutionary algorithms are estimated rigorously under some mild conditions listed in the paper. Those results in this paper are commonly useful. Also, the analytic techniques adopted in the paper are widely instructive for analyzing the computation time of evolutionary algorithms in a given search space as long as some specific mathematical arts are introduced accordingly.