Evolving symmetric and modular neural networks for distributed control

Problems such as the design of distributed controllers are character-ized by modularity and symmetry. However, the symmetries use-ful 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 prob-lems. It abstracts properties of generative and developmental sys-tems, and utilizes group theory to represent symmetry and search for it systematically, making it more evolvable than randomly mu-tating 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 evolv-ing such controllers than random symmetry mutations. Thus, ENSO is a promising approach for evolving modular and symmetric solu-tions to distributed control problems, as well as multiagent systems in general