Here we will discuss the framework within which GAs are typically used, before going on to suggest that for many hardware design problems a significantly different framework is needed.
The majority of published GA work, both applications and theoretical analysis, refers to optimisation problems which can be seen as search problems in some high-dimensional search space, of known (usually enormous) size. The components to be optimised could be parameters which need to be set at appropriate real values; or they could be discrete values which need to be chosen. In the former case the real values needed are usually coded to some desired degree of precision, so that they can be specified in binary form with a defined number of bits (although some evolutionary algorithms work directly with real values).
What such optimisation problems share is the well-defined finite dimensionality of the search space. This allows the choice of some genotype coding, such that a genotype (often binary) of fixed length can encode any potential solution within the space of possibilities. In the context of hardware design, this approach is appropriate where the optimal attributes for a predetermined number of components is to be found; also where the ordering of any given set of components needs to be determined.
GA theory has in general assumed such a fixed-dimensional search space. The optimisation problem has typically been seen as starting with a population of random points effectively spanning and coarsely sampling the whole search space. Successive rounds of selection, reproduction and mutation are intended to focus the population of sample points towards fitter regions of the space, homing in on an optimum or near-optimal region. Theorems such as the Schema Theorem, intended to show the circumstances under which GAs can be expected to produce the desired results, rely on these assumptions. One consequence of this approach has been the primary reliance on recombination as the genetic operator, which combines information from different samples in order to move towards regions of expected higher fitness; mutation is typically treated as a background operator.
GAs can be considered a compromise between a weak and a strong form of search. While far stronger than random search, which typically is infeasible in large search spaces, GAs are not strong enough for one to be able to demonstrate conclusively that the global optimum has been reached. Once recombination has brought the population, over a number of generations, into a focused region of search space -- i.e. it is genetically converged -- then with only background rates of mutation further exploration cannot be expected, and search can be terminated. If this convergence happens too rapidly, it implies that only a sketchy sampling of the search space has been done, and any local optimum reached may be far from the global optimum. Much GA analysis is directed towards setting up the GA parameters so as to avoid this premature convergence.
However, some problems -- including perhaps most hardware design problems -- do not fall into this convenient picture of a fixed-dimensional search space. If there is no predetermined number of components to be used in the design then standard GA theory will not apply.