Metaheuristics by Patrick Siarry

Author:Patrick Siarry
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(9.15)

Fig. 9.7Relationship between species count, immigration rate, and emigration rate

For the sake of simplicity, the original BBO considered a linear migration model (Fig. 9.7) where the immigration rate and the emigration rate are linear functions of the number of species S in the habitat, but different mathematical models of biogeography that include more complex variables are presented in [55]. There are in fact other important factors which influence migration rates between habitats, including the distance to the nearest neighboring habitat, the size of the habitat, climate (temperature and precipitation), plant and animal diversity, and human activity. These factors make immigration and emigration curves complicated, unlike those described in the original BBO paper [86]. To study the influence of different migration models on the performance of BBO, Haiping Ma [54] explored the behavior of six different migration models and investigates the performance on 23 benchmark functions with a wide range of dimensions and diverse complexities. The experimental results clearly showed that different migration models resulted in significant changes in performance, and BBO migration models which were closer to nature (that is, nonlinear) were significantly better than linear models for most of the benchmarks.

We now consider the probability that the habitat contains exactly S species. The number of species will change from time t to time as follows:

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