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Mathematical Problems in Engineering
Volume 2013, Article ID 353969, 20 pages
Research Article

Biogeography-Based Optimization with Orthogonal Crossover

1Department of Applied Mathematics, Xidian University, Xi’an 710071, China
2School of Science, Guilin University of Technology, Guilin 541004, China
3School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China

Received 6 January 2013; Revised 15 April 2013; Accepted 15 April 2013

Academic Editor: Alexander P. Seyranian

Copyright © 2013 Quanxi Feng 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.


Biogeography-based optimization (BBO) is a new biogeography inspired, population-based algorithm, which mainly uses migration operator to share information among solutions. Similar to crossover operator in genetic algorithm, migration operator is a probabilistic operator and only generates the vertex of a hyperrectangle defined by the emigration and immigration vectors. Therefore, the exploration ability of BBO may be limited. Orthogonal crossover operator with quantization technique (QOX) is based on orthogonal design and can generate representative solution in solution space. In this paper, a BBO variant is presented through embedding the QOX operator in BBO algorithm. Additionally, a modified migration equation is used to improve the population diversity. Several experiments are conducted on 23 benchmark functions. Experimental results show that the proposed algorithm is capable of locating the optimal or closed-to-optimal solution. Comparisons with other variants of BBO algorithms and state-of-the-art orthogonal-based evolutionary algorithms demonstrate that our proposed algorithm possesses faster global convergence rate, high-precision solution, and stronger robustness. Finally, the analysis result of the performance of QOX indicates that QOX plays a key role in the proposed algorithm.