In artificial evolution problems of varying dimensionality one should expect to have a genetically converged population, in effect a species, at all times. This contrasts with optimisation problems, where convergence in a GA signals the end of the search process. Using the example given above, where a hardware design being evolved could potentially have any number of components up to 20, during any single generation one should expect all the members of the population to have the same or a very similar number of components, for instance 10. What counts as similarity will be qualified later.
The conceptual framework of SAGA was introduced by Harvey in 1991 in order to try to understand the dynamics of a GA when genotype lengths are allowed to increase [4]. It was shown, using concepts of epistasis and fitness landscapes drawn from theoretical biology [5], that progress through such a genotype space will only be feasible through relatively gradual increases in information in the genotype (typically, in genotype length). A general trend towards increase in length is associated with the evolution of a species rather than global search. Such evolutionary search in the space of hardware designs would be from initially simple designs for simple tasks, towards more complex designs for more complex tasks; although in natural evolution there is no externally provided sense of direction, in artificial evolution this can be provided.
Throughout such artificial evolution, a species will be relatively fit, in the sense that most members of the population will be fitter than most of their neighbours in the fitness landscape. Evolutionary search can be thought of as searching around the current focus of a species for neighbouring regions which are fitter (or in the case of neutral drift, not less fit) while being careful not to lose gains that were made in achieving the current status quo. In the absence of any mutation (or change-length) genetic operator, selection will concentrate the population at the current best. The smallest amount of mutation will hill-climb this current best to a local optimum. As mutation rates increase, the population will spread out around this local optimum, searching the neighbourhood; but if mutation rates become too high then the population will disperse completely, losing the hill-top, and the search will become random. If an ideal balance is achieved between selective forces and those of mutation (as modified by recombination), then some elements of the population can crawl down the hill far enough to reach a ridge of relatively high selective values. As discussed in [6], this results in a significant proportion of the population working their way along this ridge under selection, and making possible the reaching of outliers ever further in Hamming-distance in that particular direction from the current fittest. The term `ridge' is used here to fit in with intuitive notions of fitness landscapes; in fact in high-dimensional search spaces such ridges may form complex neutral networks, percolating long distances through genotype space.
If any such outliers reach a second hill that climbs away from the ridge, then parts of the population can climb this hill. Depending on the difference in fitness and the spread of the population, it will either move en masse to the new hill as a better local optimum, or share itself across both of them.
So in a SAGA setup of evolution of a converged species, we want to encourage through the genetic operators such exploration along ridges to new hills, subject to the constraint that we do not want to lose track of the current hill. Eigen and co-workers use the concept of a quasi-species to refer to a similar genetically converged population in the study of early RNA evolution. To quote from [6]:
In conventional natural selection theory, advantageous mutations drove the evolutionary process. The neutral theory introduced selectively neutral mutants, in addition to the advantageous ones, which contribute to evolution through random drift. The concept of quasi-species shows that much weight is attributed to those slightly deleterious mutants that are situated along high ridges in the value landscape. They guide populations toward the peaks of high selective values.