Markov
Analysis of Biogeography-Based Optimization

Dan
Simon, Mehmet Ergezer, and Dawei Du

Biogeography is the study of the geographical distribution of biological organisms. The mindset of the engineer is that we can learn from nature. This motivates the application of biogeography to optimization problems. An introduction to biogeography-based optimization (BBO) can be found at http://academic.csuohio.edu/simond/bbo. The references below discusses how Markov analysis can be used to analytically obtain the probability of each possible population in a BBO problem.

The software that was used to create the results in [1] can be
downloaded in a zip file. The software is written in m-files that can be run in
the MATLAB environment. The m-files are
contained in bbomarkov.zip. If you
download the zip file to your hard drive and then unzip the file, you can
reproduce the results in [1]. Maybe you can even modify the m-files for
your own research. When you unzip the file on your hard drive, look at **readme.txt** for more detailed
information.

*References*

- D. Simon, M. Ergezer, D. Du, and R. Rarick, Markov models for biogeography-based optimization, IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics, vol. 41, no. 1, pp. 299-306, January 2011 – This paper is probably the most complete description that we have of BBO Markov modeling
- D. Simon, M. Ergezer, and D. Du, Population distributions in biogeography-based optimization algorithms with elitism, IEEE Conference on Systems, Man, and Cybernetics, San Antonio, Texas, pp. 1017-1022, October 2009 – This is a preliminary version of the above paper, but this paper also shows how to include elitism in the Markov model
- D. Simon, R. Rarick, M. Ergezer, and D. Du, Analytical and numerical comparisons of biogeography-based optimization and genetic algorithms, Information Sciences, vol. 181, no. 7, pp. 1224-1248, April 2011 - This paper uses Markov models to obatin analytical comparisons of BBO and genetic algorithms
- D. Simon, The Dimension of an Evolutionary Algorithm Transition Matrix, June 2009 - This unpublished note shows some different ways to calculate the dimension of the Markov transition matrix. It applies to Markov modeling for any evolutionary algorithm, not just for BBO.

Department of Electrical and Computer Engineering

Last Revised: September 14, 2011