On Appropriate Adaptation Levels for the Learning of Gene Linkage

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.