The mesh-connected architecture is widely used in multi-computers and computer networks for parallel and distributed computing. In such architectures each executor (processor or computer) has up to four neighbors. This condition can be naturally (physically) met in dedicated supercomputers, but the problem arises when there is a need to implement this architecture for computer networks, such as Internet, where each computer is connected to each other. The aim of this work is to provide an algorithm to create an efficient mesh-structure, choosing the best possible connections between considered nodes of a computer network. The proposed algorithms AGAMS is based on the genetic algorithm idea. Some results of investigations of properties of AGAMS are discussed.