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Mathematical Problems in Engineering
Volume 2013, Article ID 682073, 14 pages
Research Article

Lévy-Flight Krill Herd Algorithm

1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China
2University of Chinese Academy of Sciences, Beijing 100039, China
3Department of Civil Engineering, University of Akron, Akron, OH 44325­3905, USA
4Department of Civil and Environmental Engineering, Engineering Building, Michigan State University, East Lansing, MI 48824, USA
5School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China

Received 3 November 2012; Accepted 20 December 2012

Academic Editor: Siamak Talatahari

Copyright © 2013 Gaige Wang 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.


To improve the performance of the krill herd (KH) algorithm, in this paper, a Lévy-flight krill herd (LKH) algorithm is proposed for solving optimization tasks within limited computing time. The improvement includes the addition of a new local Lévy-flight (LLF) operator during the process when updating krill in order to improve its efficiency and reliability coping with global numerical optimization problems. The LLF operator encourages the exploitation and makes the krill individuals search the space carefully at the end of the search. The elitism scheme is also applied to keep the best krill during the process when updating the krill. Fourteen standard benchmark functions are used to verify the effects of these improvements and it is illustrated that, in most cases, the performance of this novel metaheuristic LKH method is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods. Especially, this new method can accelerate the global convergence speed to the true global optimum while preserving the main feature of the basic KH.