  Geometric crossover is a representation-independent definition 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
recombination operators for the most frequently used representations. Using a
distance tailored to the problem at hand, the abstract definition of crossover
can be used to design new problem 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.
