Model Analysis and Application Case for Complex Multi-System Evolutionary Optimization

A complex system is made up of multiple related and coupled subsystems. Each subsystem has its own set of multiple constraints and objectives, and is commonly found in real-world applications. Biogeography-based complex system optimization (BBO/Complex) is a population-based evolutionary intelligence paradigm that has been developed to solve complex system problems. The paper first presents the framework of the proposed method that consists of within-subsystem migration, cross-subsystem migration, and mutation operators. Then a theoretical model of the proposed method is derived using Markov chain and the probability transition matrix of each operator, along with the generalized multinomial theorem. The model provides exact mathematical formulas that predict the limiting probabilities of optimization performance for each possible population in the proposed method. Additionally, simulation results of two sample problems, which include multiple subsystems and multiple objectives, confirm the Markov model derived. Finally, the performance of the proposed method is investigated on an application of a battery charging system, and numerical simulation shows that the proposed method is a promising optimization method for the studied complex system.