Bio-inspired Network Optimization Based on Semi-Definite Programming

Modern society is a networked society. To design or build a network, one has to consider the cost of building it, the efficiency of transmission of information, resources, energy or man in the network, and the fault tolerance when some nodes and pathways in the network fail. These requirements are often mutually restricted. In order to design optimized network, this paper formulate a novel semi-definite programming (SDP) problem. First, a new objective function is designed, which constitutes of the total network length and the determinant of the network Laplacian. Then, the constraints of the SDP is proposed as the flux rules and node rules of a bio-inspired optimization algorithm. Finally, The proposed algorithm is validated by numerical examples.