Evolutionary optimised consensus and synchronisation networks

Abstract

There is consensus problem as an important characteristic for coordinated control problem in collective behaviour, the interaction between agents and factors. 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 their characteristics have been investigated. But in this study, network is evolved to suit the characteristics of the objection by evolutionary algorithm and we create optimised network. As a function of the adaptive optimisation, we consider the objection that combine consensus, synchronisation index and the density of the link, and create the optimised network which is suitable to the property of the objective function by evolutionary algorithms. Optimal networks that we have designed have better synchronisation and consensus property in terms of the convergence speed and network eigenvalues. We show that the convergence speed is faster in evolutionary optimised networks than previous networks which are known as better synchronisation networks. As a result, we generate optimal consensus and synchronous network.