An Efficient Distance Metric for Linear Genetic Programming

Defining a distance measure over the individuals in the population of an Evolutionary Algorithm can be exploited for several applications, ranging from diversity preservation to balancing exploration and exploitation. When individuals are encoded as strings of bits or sets of real values, computing the distance between any two can be a straightforward process; when individuals are represented as trees or linear graphs, however, quite often the user must resort to phenotype-level problem-specific distance metrics. This paper presents a generic genotype-level distance metric for Linear Genetic Programming: the information contained by an individual is represented as a set of symbols, using n-grams to capture significant recurring structures inside the genome. The difference in information between two individuals is evaluated resorting to a symmetric difference. Experimental evaluations show that the proposed metric has a strong correlation with phenotype-level problem-specific distance measures in two problems where individuals represent string of bits and Assembly-language programs, respectively.