Evolving symmetric and modular neural networks for distributed control

Problems such as the design of distributed controllers are characterized by modularity and symmetry. However, the symmetries useful for solving them are often difficult to determine analytically. This paper presents a nature-inspired approach called Evolution of Network Symmetry and mOdularity (ENSO) to solve such problems. It abstracts properties of generative and developmental systems, and utilizes group theory to represent symmetry and search for it systematically, making it more evolvable than randomly mutating symmetry. This approach is evaluated by evolving controllers for a quadruped robot in physically realistic simulations. On flat ground, the resulting controllers are as effective as those having hand-designed symmetries. However, they are significantly faster when evolved on inclined ground, where the appropriate symmetries are difficult to determine manually. The group-theoretic symmetry mutations of ENSO were also significantly more effective at evolving such controllers than random symmetry mutations. Thus, ENSO is a promising approach for evolving modular and symmetric solutions to distributed control problems, as well as multiagent systems in general.