Optimal Network Design for Consensus Formation: Wisdom of Networked Agents

The wisdom of crowds refers to the phenomenon in which the collective knowledge of a community is greater than the knowledge of any individual. This paper proposes a network design for the fastest and slowest consensus formation under average node degree restrictions, which is one aspect of the wisdom of crowds concept. Consensus and synchronization problems are closely related to variety of issues such as collective behavior in nature, the interaction among agents as a matter of the robot control, and building efficient wireless sensor networks. However, designing networks with desirable properties is complex and it may pose a multi-constraint and multi-criterion optimization problem. For the purpose of realizing such efficient network topology, this paper presents an optimization approach to design networks for better consensus formation by focusing on the eigenvalue spectral of Laplacian matrix. In both the fastest and slowest networks presented, consensus is formed among local structures first, then on a global scale. This suggests that both local and global topology influence the networks dynamics. These findings are useful for those who seek to manage efficient consensus and synchronization in a setting that can be modeled as a multi-agent system. Keywords—wisdom of crowds; consensus problem; Laplacian