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Focusing versus Intransitivity
Geometrical Aspects of Co-evolution
Anthony Bucci* and Jordan B. Pollack
Brandeis University, Waltham MA 02454, USA
{abucci,pollack}@cs.brandeis.edu
http://demo.cs.brandeis.edu/
Abstract.
Recently, a minimal domain dubbed the numbers game has been proposed
to illustrate well-known issues in co-evolutionary dynamics. The domain
permits controlled introduction of features like intransitivity, allowing
researchers to understand failings of a co-evolutionary algorithm in terms
of the domain. In this paper, we show theoretically that a large class of
co-evolution problems closely resemble this minimal domain. In particular,
all the problems in this class can be embedded into an ordered,
-dimensional Euclidean space, and so can be construed as greater-than
games. Thus, conclusions derived using the numbers game are more widely
applicable than might be presumed. In light of this observation, we present
a simple algorithm aimed at remedying focusing problems and relativism in
the numbers game. With it we show empirically that, contrary to
expectations, focusing in
transitive games can be more troublesome for co-evolutionary
algorithms than intransitivity. Practitioners should therefore be just as
wary of focusing issues in application domains.
*Corresponding author
LNCS 2723, p. 250 ff.
lncs@springer.de
© Springer-Verlag Berlin Heidelberg 2003