Reliable Swarm Design

This paper describes how phase space diagrams may be used to predict the final states and system evolution of swarms. Phase space diagrams and system evolutions through phase space are constructed for systems of multiple and single attractors. While the diagrams indicate the number of attractors, the system evolutions confirm them. A method is described for generating stochastic differential equations, which can then be used to construct phase space diagrams. This method is applied to the TSP system update equations, generating a stochastic differential equation whose dynamics provide insight into the TSP system. The use of ensemble system updates transforms systems from directed random walk systems to systems governed by stochastic differential equations. We demonstrate the use on the puck clustering and TSP problems, generating improved reliability and quick evolution of the system.