A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space



Geometric crossover is a representation-independent defini-
tion of crossover based on the distance of the search space
interpreted as a metric space. It generalizes the traditional
crossover for binary strings and other important recombina-
tion operators for the most frequently used representations.
Using a distance tailored to the problem at hand, the ab-
stract definition of crossover can be used to design new prob-
lem specific crossovers that embed problem knowledge in the
search. This paper is motivated by the fact that genotype-
phenotype mapping can be theoretically interpreted using
the concept of quotient space in mathematics. In this paper,
we study a metric transformation, the quotient metric space,
that gives rise to the notion of quotient geometric crossover.
This turns out to be a very versatile notion. We give many
example applications of the quotient geometric crossover.


Seoul National University Technical Report, January 2009

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