1. TITLE
 	"Reinventing the Wheel: An Experiment in Evolutionary Geometry"

2. 	Josh Bongard
  	Upson Hall, Cornell University, Ithaca, NY, 14850, USA
	josh.bongard@cornell.edu
	(607) 339-9948

	Hod Lipson
	Upson Hall, Cornell University, Ithaca, NY, 14850, USA
	hod.lipson@cornell.edu
	(607) 255-1686

3. CORRESPONDING AUTHOR

Josh Bongard

4. ABSTRACT

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.

5.MATCHING CRITERIA: A, F, G

6. STATEMENT

Although the wheel now seems like a commonplace and simple mechanical device, it was unarguably the most important invention of human civilization. Despite its simplicity, the wheel was not discovered by several civilizations, including those in Australia, sub-Saharan Africa, and the Americas. Moreover, from the discovery of the wheel in about the 5th millenium BC, it took nearly 7000 years to discover that the wheel is not the only shape that can be used for transporting objects smooth over flat terrain. When posed to an evolutionary algorithm, it discovers not just the wheel, but several members of curves of constant length, which successfully can be used to transport objects over flat terrain. This result is competitive because it discovers in less than one hour what it took combined humanity 7000 years to discover. More specifically,

(A) "The result was patented as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention."

The wheel was patented as a "circular transportation facilitation device" by John Keogh, an Australian patent lawyer, in July 2001.

(F) "The result is equal to or better than a result that was considered an achievement in its field at the time it was first discovered."

The wheel was definitely an achievement when it was discovered, as it led to advantages in trade, warface, and agriculture. The result is better than the initial discovery of the wheel because our algorithm not only discovers the wheel, but other non-circular shapes that can also serve as wheels.

(G) "The result solves a problem of indisputable difficulty in its field."

The result solves a very difficult problem (historically), which is how to transport objects over flat ground with zero vertical motion induced in the objects.

7. CITATION
Bongard, J., Lipson, H. "Reinventing the Wheel: An Experiment in Evolutionary Geometry", Late Breaking Papers of the 2005 Genetic and Evolutionary Computation Conference, Washington, DC, June 2005.