Evolutionary Computation with Biogeography-based Optimization

7Statistical Mechanics Approximations of BBO

In the previous two chapters, we set up the Markov model and dynamic system model of BBO to analyze the behavior of BBO. Those models tell us the exact probability distribution over all possible populations, but in practice, those models rapidly become impractical as the size of the search space grows, which limits their application to very small problems. This is the curse of dimensionality for analytical EA models. It is therefore natural to investigate other methods to obtain practical models. The statistical mechanics approximation is used in this chapter to analyze the behavior of BBO. The idea of this modeling approach comes from the field of statistical mechanics, which involves averaging the behavior of many molecular particles to model the behavior of a group of molecules. We can use this idea to model BBO behavior with large populations and to better understand the evolution of BBO in realistic, high-dimensional optimization problems.

Overview of the chapter

In this chapter, we will see that statistical mechanics approximation theory provides insight into BBO behavior. Section 7.1 provides the preliminary foundation for statistical mechanics approximations. Section 7.2 derives a statistical mechanics model for the basic BBO algorithm. Section 7.3 discusses extensions of the BBO statistical mechanics model.

7.1. Preliminary foundation

Statistical mechanics is a branch of physics that applies probability theory to the study ...