4 Genetic Outlier Definition

Figure 7.1 shows the divisions of the phenotype and genotype space used to define genetic outliers. To investigate where future populations come from, the definition of genetic outlier used here is based on the properties of selection and similarity. Selection is based on fitness, thus the population is divided into those individuals which are better-than more than half of the population. The better-than relationship describes the case where selection will always pick one individual over the other. This subpopulation is called the fit subpopulation. The subpopulation that is left is called the un-fit.

Next, the fit subpopulation is further divided into the similar and the dissimilar. The Levenshtein distance between strings, or string edit distance, is used to define the distance between structures. The structure is represented by a breadth-first traversal of trees with node labels $\in$ [n,l]. This is the same distance measure used in previous chapters, called edit distance one, except trees only consist of the symbols `n' and `l'. Each individual's pair-wise distance is the average edit distance to the rest of the population, where each distance is normalised by dividing by the the larger size of the pair of trees. The mean pair-wise distance of the population is then found by dividing the summation of all individual pair-wise distance's by the population size. The subpopulation that is better-than half the population, the fit subpopulation, is then further divided into those which have a pair-wise distance to the population that is less than or equal to two-standard deviations from the population's mean pair-wise distance. This subpopulation is called the in-liers. The subpopulation that is left is called the outliers, which are genetically different from the rest and better-than more than half the population.

Figure 7.3: The pareto front and points visited for the Tree-String experiments.