Extended Species Abundance Models of Biogeography Based Optimization

This paper is an extension to the models of species abundance in biogeography based optimization technique. We present the extended species abundance models by defining the parameter species growth rate as a function of species evolution rate and the species immigration rate and species decline rate as a function of species extinction rate and emigration rate for the determination of the total species count at a given time instant on a single habitat, as opposed to the Simon's model which relies upon migration only for the determination of the species count. We also introduce an additional dependency factor which signifies the interdependence of migrating species on each other such as the predator-prey relationships, to be considered for the determination of immigration and emigration rates and hence further extend the original model of species abundance in a single habitat. We discuss the extended BBO and its mathematics and then go on to present the extended forms of each of the six representative migration models that were originally proposed by Haiping Ma as an extension to the work by Simon. We demonstrate the performance of each of the extended models of BBO by running them on standard benchmark functions and found that the average convergence of each of the proposed extended species abundance models is faster leading to better optimization results than the original species abundance model of BBO.