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Computational Intelligence and Neuroscience
Volume 2015 (2015), Article ID 485215, 8 pages
Research Article

An Analytical Framework for Runtime of a Class of Continuous Evolutionary Algorithms

School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, China

Received 26 May 2015; Accepted 26 July 2015

Academic Editor: Manuel Graña

Copyright © 2015 Yushan Zhang and Guiwu Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Although there have been many studies on the runtime of evolutionary algorithms in discrete optimization, relatively few theoretical results have been proposed on continuous optimization, such as evolutionary programming (EP). This paper proposes an analysis of the runtime of two EP algorithms based on Gaussian and Cauchy mutations, using an absorbing Markov chain. Given a constant variation, we calculate the runtime upper bound of special Gaussian mutation EP and Cauchy mutation EP. Our analysis reveals that the upper bounds are impacted by individual number, problem dimension number , searching range, and the Lebesgue measure of the optimal neighborhood. Furthermore, we provide conditions whereby the average runtime of the considered EP can be no more than a polynomial of . The condition is that the Lebesgue measure of the optimal neighborhood is larger than a combinatorial calculation of an exponential and the given polynomial of .