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.

Videos of the evolved robot walking behaviors