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Mathematical Problems in Engineering
Volume 2014, Article ID 147457, 11 pages
Research Article

On the Convergence of Biogeography-Based Optimization for Binary Problems

1Department of Electrical Engineering, Shaoxing University, Shaoxing, Zhejiang, China
2Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China
3Department of Electrical and Computer Engineering, Cleveland State University, Cleveland, OH 44115, USA

Received 28 January 2014; Accepted 1 May 2014; Published 22 May 2014

Academic Editor: Erik Cuevas

Copyright © 2014 Haiping Ma 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 an evolutionary algorithm inspired by biogeography, which is the study of the migration of species between habitats. A finite Markov chain model of BBO for binary problems was derived in earlier work, and some significant theoretical results were obtained. This paper analyzes the convergence properties of BBO on binary problems based on the previously derived BBO Markov chain model. Analysis reveals that BBO with only migration and mutation never converges to the global optimum. However, BBO with elitism, which maintains the best candidate in the population from one generation to the next, converges to the global optimum. In spite of previously published differences between genetic algorithms (GAs) and BBO, this paper shows that the convergence properties of BBO are similar to those of the canonical GA. In addition, the convergence rate estimate of BBO with elitism is obtained in this paper and is confirmed by simulations for some simple representative problems.