Evolutionary optimized networks for consensus and synchronization

Abstract

Collective behavior in nature, the interaction between agents and factors, there is consensus problem as an important characteristic for coordinated control problem. Consensus problem is closely related to the complex networks. Recently, many studies are being considered in the complex network structure, the question what network is the most suitable to the property of the purpose has not been answered yet in many areas. In the previous study, network model has been created under the regular rules, and investigated their characteristics. But in this study, network is evolved to suit the characteristics of the objection by evolutionary algorithm and we create optimized network. As a function of the adaptive optimization, we consider the objection that combinate consensus, synchronization index and the density of the link, and create the optimized network which is suitable to the property of the objective function by evolutionary algorithms. Optimal networks that we design have better synchronization and consensus property in terms of the convergence speed and network eigenvalues. We show that the convergence speed is faster in evolutionary optimized networks than previous networks which are known as better synchronization networks. As a result, we generate optimal consensus and synchronous network. © 2010 Springer-Verlag Berlin Heidelberg.