DocumentCode :
1203289
Title :
A New Approach for Analyzing Average Time Complexity of Population-Based Evolutionary Algorithms on Unimodal Problems
Author :
Chen, Tianshi ; He, Jun ; Sun, Guangzhong ; Chen, Guoliang ; Yao, Xin
Author_Institution :
Dept. of Comput. Sci. & Technol., Univ. of Sci. & Technol. of China, Hefei
Volume :
39
Issue :
5
fYear :
2009
Firstpage :
1092
Lastpage :
1106
Abstract :
In the past decades, many theoretical results related to the time complexity of evolutionary algorithms (EAs) on different problems are obtained. However, there is not any general and easy-to-apply approach designed particularly for population-based EAs on unimodal problems. In this paper, we first generalize the concept of the takeover time to EAs with mutation, then we utilize the generalized takeover time to obtain the mean first hitting time of EAs and, thus, propose a general approach for analyzing EAs on unimodal problems. As examples, we consider the so-called (N + N) EAs and we show that, on two well-known unimodal problems, leadingones and onemax , the EAs with the bitwise mutation and two commonly used selection schemes both need O(nlnn + n 2/N) and O(n lnlnn + nlnn/N) generations to find the global optimum, respectively. Except for the new results above, our approach can also be applied directly for obtaining results for some population-based EAs on some other unimodal problems. Moreover, we also discuss when the general approach is valid to provide us tight bounds of the mean first hitting times and when our approach should be combined with problem-specific knowledge to get the tight bounds. It is the first time a general idea for analyzing population-based EAs on unimodal problems is discussed theoretically.
Keywords :
computational complexity; evolutionary computation; statistical analysis; average time complexity; bitwise mutation; generalized takeover time; mean first hitting time; population-based evolutionary algorithm; selection scheme; unimodal problem; Drift analysis; evolutionary algorithms (EAs); first hitting time; takeover time; unimodal problems; Algorithms; Artificial Intelligence; Computer Simulation; Models, Genetic; Models, Theoretical; Pattern Recognition, Automated;
fLanguage :
English
Journal_Title :
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on
Publisher :
ieee
ISSN :
1083-4419
Type :
jour
DOI :
10.1109/TSMCB.2008.2012167
Filename :
4804707
Link To Document :
بازگشت