Abstract
A number of algorithms have been proposed aimed at
tackling the problem of learning Gene Linkage within
the context of genetic optimisation, that is to say,
the problem of learning which groups of co-adapted
genes should be inherited together during the
recombination process. These may be seen within a wider
context as a search for appropriate relations which
delineate the search space and guide heuristic
optimisation, or, alternatively, as a part of a
comprehensive body of work into Adaptive Evolutionary
Algorithms.
In this paper, we consider the learning of Gene Linkage
as an emergent property of adaptive recombination
operators. This is in contrast to the behaviour
observed with fixed recombination strategies in which
there is no correspondence between the sets of genes
which are inherited together between generations, other
than that caused by distributional bias. A discrete
mathematical model of Gene Linkage is introduced, and
the common families of recombination operators, along
with some well known linkage-learning algorithms, are
modelled within this framework. This model naturally
leads to the specification of a recombination operator
that explicitly operates on sets of linked
genes.
Variants of that algorithm, are then used to examine
one of the important concepts from the study of
adaptivity in Evolutionary Algorithms, namely that of
the level (population, individual, or component) at
which learning takes place. This is an aspect of
adaptation which has received considerable attention
when applied to mutation operators, but which has been
paid little attention in the context of adaptive
recombination operators and linkage learning. It is
shown that even with the problem restricted to learning
adjacent linkage, the population based variants are not
capable of correctly identifying building blocks. This
is in contrast to component level adaptation which
outperforms conventional operators whose bias is ideal
for the problems considered.
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