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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 135652, 11 pages
Research Article

A Convergent Differential Evolution Algorithm with Hidden Adaptation Selection for Engineering Optimization

1School of Computer Science and Technology, Wuhan University of Technology, Wuhan, Hubei 430070, China
2School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei 432000, China
3State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430072, China

Received 27 November 2013; Revised 25 January 2014; Accepted 27 February 2014; Published 30 March 2014

Academic Editor: Gongnan Xie

Copyright © 2014 Zhongbo Hu et al. 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.


Many improved differential Evolution (DE) algorithms have emerged as a very competitive class of evolutionary computation more than a decade ago. However, few improved DE algorithms guarantee global convergence in theory. This paper developed a convergent DE algorithm in theory, which employs a self-adaptation scheme for the parameters and two operators, that is, uniform mutation and hidden adaptation selection (haS) operators. The parameter self-adaptation and uniform mutation operator enhance the diversity of populations and guarantee ergodicity. The haS can automatically remove some inferior individuals in the process of the enhancing population diversity. The haS controls the proposed algorithm to break the loop of current generation with a small probability. The breaking probability is a hidden adaptation and proportional to the changes of the number of inferior individuals. The proposed algorithm is tested on ten engineering optimization problems taken from IEEE CEC2011.