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An analysis of the equilibrium of migration models for biogeography-based optimization. (English) Zbl 1194.92073
Summary: Motivated by the migration mechanisms of ecosystems, various extensions to biogeography-based optimization (BBO) are proposed here. As a global optimization method, BBO is an original algorithm based on the mathematical model of organism distribution in biological systems. BBO is an evolutionary process that achieves information sharing by biogeography-based migration operators. In BBO, habitats represent candidate problem solutions, and species migration represents the sharing of features between candidate solutions according to the fitness of the habitats.
This paper generalizes equilibrium species count results in biogeography theory, explores the behavior of six different migration models in BBO, and investigates performance through 23 benchmark functions with a wide range of dimensions and diverse complexities. The performance study shows that sinusoidal migration curves provide the best performance among the six different models that we explored. In addition, comparison with other biology-based optimization algorithms is investigated, and the influence of the population size, problem dimension, mutation rate, and maximum migration rate of BBO are also studied.

92D40 Ecology
90C90 Applications of mathematical programming
91D20 Mathematical geography and demography
Full Text: DOI
[1] Bergh, F.; Engelbrecht, A.P., A study of particle swarm optimization particle trajectories, Information sciences, 176, 8, 937-971, (2006) · Zbl 1093.68105
[2] Bhattacharya, A.; Chattopadhyay, P., Solving complex economic load dispatch problems using biogeography-based optimization, Expert systems with applications, 37, 5, 3605-3615, (2010)
[3] Blum, C., Ant colony optimization: introduction and recent trends, Physics of life reviews, 2, 353-373, (2005)
[4] Clerc, M.; Kennedy, J., The particle swarm explosion, stability, and convergence in a multidimensional complex space, IEEE transactions on evolutionary computation, 6, 58-73, (2002)
[5] Darwin, C., The origin of species, (1995), Gramercy New York, USA, (first published in 1859)
[6] Dorigo, M.; Maniczzo, V.; Colomi, A., Ant system: optimization by a colony of cooperating agents, IEEE transaction on systems, man, and cybernetics part B, 26, 29-41, (1996)
[7] Du, W.; Li, B., Multi-strategy ensemble particle swarm optimization for dynamic optimization, Information sciences, 178, 15, 3096-3109, (2008) · Zbl 1283.90047
[8] D.W. Du, D. Simon, M. Ergezer, Biogeography-based optimization combined with evolutionary strategy and immigration refusal, in: Proceedings of the IEEE Conference on Systems, Man, and Cybernetics, San Antonio, TX, 2009, pp. 1023-1028.
[9] Ellabib, I.; Calamai, P.; Basir, O., Exchange strategies for multiple ant colony system, Information sciences, 177, 5, 1248-1264, (2007)
[10] M. Ergezer, D. Simon, D.W. Du, Oppositional biogeography-based optimization, in: Proceeding of IEEE the Conference on Systems, Man, and Cybernetics, San Antonio, TX, 2009, pp. 1035-1040.
[11] Gong, D.; Yao, X.; Yuan, J., Interactive genetic algorithms with individual fitness not assigned by human, Journal of universal computer science, 15, 13, 2446-2462, (2009)
[12] Gustafson, S.; Burke, E., The speciating island model: an alternative parallel evolutionary algorithm, Journal of parallel and distributed computing, 66, 1025-1036, (2006) · Zbl 1102.68730
[13] Hedar, A.R.; Fukushima, M., Minimizing multimodal functions by simplex coding genetic algorithm, Optimization methods and software, 18, 265-282, (2003) · Zbl 1048.90168
[14] Ho, Y.; Pepyne, D., Simple explanation of the no-free-lunch theorem and its implications, Journal of optimization theory and applications, 115, 1573-2878, (2002) · Zbl 1031.91018
[15] Jin, Y., A comprehensive survey of fitness approximation in evolutionary computation, Soft computing - A fusion of foundations, methodologies and applications, 9, 3-12, (2005)
[16] J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proceedings of the IEEE International Conference on Neural Networks, Piscataway, NJ 1995, pp. 1942-1948.
[17] Kleidon, A., Amazonian biogeography as a test for gaia, (), 291-296
[18] H.P. Ma, S. Ni, M. Sun, Equilibrium species counts and migration model tradeoffs for biogeography-based optimization, in: Proceedings of the Combined 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, 2009, pp. 3306-3310.
[19] H.P. Ma, D. Simon, Biogeography-based optimization with blended migration for constrained optimization problems, in: Proceedings of GECCO-2010, Portland, Oregon, July, 2010.
[20] MacArthur, R.; Wilson, E., The theory of biogeography, (1967), Princeton University Press Princeton, New Jersey
[21] Michalewicz, Z., Genetic algorithms+data structures=evolution programs, (1996), Springer-Verlag London, UK · Zbl 0841.68047
[22] Muhlenbein, H.; Schlierkamp-Voosen, D., Predictive models for the breeder genetic algorithm: I. continuous parameter optimization, Evolutionary computation, 1, 25-49, (1993)
[23] M. Ovreiu, D. Simon, Biogeography-based optimization of neuro-fuzzy system parameters for diagnosis of cardiac disease, in: Proceedings of GECCO-2010, Portland, Oregon, July, 2010.
[24] Panchal, V.; Singh, P.; Kaur, N.; Kundra, H., Biogeography based satellite image classification, International journal of computer science and information security, 6, 269-274, (2009)
[25] R. Rarick, D. Simon, F.E. Villaseca, B. Vyakaranam, Biogeography-based optimization and the solution of the power flow problem, in: Proceedings of the IEEE on Systems, Man, and Cybernetics, San Antonio, Texas, 2009, pp. 1029-1034.
[26] Simon, D., Biogeography-based optimization, IEEE transactions on evolutionary computation, 12, 702-713, (2008)
[27] D. Simon, M. Ergezer, D. Du, Markov models for biogeography-based optimization and genetic algorithms with global uniform recombination, May, 2010, <http://academic.csuohio.edu/simond/bbo/markov/>.
[28] Twomey, C.; Stützle, T.; Dorigo, M.; Manfrin, M.; Birattari, M., An analysis of communication policies for homogeneous multi-colony ACO algorithms, Information sciences, 180, 12, 2390-2404, (2010)
[29] Volk, T., Gaia’s body: toward a physiology of Earth, (2003), MIT Press Cambridge, MA
[30] Wallace, A., The geographical distribution of animals, (2006), Adamant Media Corporation Boston, USA, (first published in 1876)
[31] Wang, Y.; Yang, Y., Particle swarm optimization with preference order ranking for multi-objective optimization, Information sciences, 179, 12, 1944-1959, (2009)
[32] Whittaker, R., Island biogeography, (1998), Oxford University Press Oxford, UK
[33] Whittaker, R.; Bush, M., Dispersal and establishment of tropical forest assemblages, krakatoa, Indonesia, (), 147-160
[34] Yang, Z.; Tang, K.; Yao, X., Large scale evolutionary optimization using cooperative coevolution, Information sciences, 178, 15, 2985-2999, (2008) · Zbl 1283.65064
[35] Yao, X.; Liu, Y.; Lin, G., Evolutionary programming made faster, IEEE transactions on evolutionary computation, 3, 82-102, (1999)
[36] Yuan, Q.; Qian, F.; Du, W., A hybrid genetic algorithm with the Baldwin effect, Information sciences, 180, 5, 640-652, (2010) · Zbl 1187.68570
[37] Zhao, S.Z.; Suganthan, P.N., Multi-objective evolutionary algorithm with ensemble of external archives, International journal of innovative computing, information and control, 6, 1, 1713-1726, (2010)
[38] Zhou, Z.; Ong, Y.S.; Nair, P.B.; Keane, A.J.; Lum, K.Y., Combining global and local surrogate models to accelerate evolutionary optimization, IEEE transactions on systems, man, and cybernetics, part C: applications and reviews, 37, 66-76, (2007)
[39] Y. Zhu, Z. Yang, J. Song, A genetic algorithm with age and sexual features, in: Proceedings of International Conference on Intelligent Computing, Kunming, China, 2006, pp. 634-640.
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