Hod Lipson: Reinventing the Wheel: An Experiment in Evolutionary Geometry

http://ccsl.mae.cornell.edu/papers/GECCO05_Bongard2.pdf

In the domain of design, there are two ways of viewing the competitiveness
of evolved structures: they either improve in some manner
on previous solutions; they produce alternative designs that were
not previously considered; or they achieve both. In this paper we
show that the way in which designs are genetically encoded influences
which alternative structures are discovered, for problems in
which a set of more than one optimal solution exists. The problem
considered is one of the most ancient known to humanity: design
a two-dimensional shape that, when rolled across flat ground,
maintains a constant height. It was not until the late 19th century—
roughly 7000 years after the discovery of the wheel—that Franz
Reuleaux showed that a circle is not the only optimal solution. Here
we demonstrate that artificial evolution repeats this discovery in under
one hour.