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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 1423930, 22 pages
Research Article

Lévy-Flight Moth-Flame Algorithm for Function Optimization and Engineering Design Problems

1College of Information Science and Engineering, Guangxi University for Nationalities, Nanning 530006, China
2Key Laboratory of Guangxi High Schools Complex System and Computational Intelligence, Nanning 530006, China

Received 18 April 2016; Accepted 12 July 2016

Academic Editor: Jose J. Muñoz

Copyright © 2016 Zhiming Li 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.


The moth-flame optimization (MFO) algorithm is a novel nature-inspired heuristic paradigm. The main inspiration of this algorithm is the navigation method of moths in nature called transverse orientation. Moths fly in night by maintaining a fixed angle with respect to the moon, a very effective mechanism for travelling in a straight line for long distances. However, these fancy insects are trapped in a spiral path around artificial lights. Aiming at the phenomenon that MFO algorithm has slow convergence and low precision, an improved version of MFO algorithm based on Lévy-flight strategy, which is named as LMFO, is proposed. Lévy-flight can increase the diversity of the population against premature convergence and make the algorithm jump out of local optimum more effectively. This approach is helpful to obtain a better trade-off between exploration and exploitation ability of MFO, thus, which can make LMFO faster and more robust than MFO. And a comparison with ABC, BA, GGSA, DA, PSOGSA, and MFO on 19 unconstrained benchmark functions and 2 constrained engineering design problems is tested. These results demonstrate the superior performance of LMFO.