Geometricity of genetic operators for real-coded representation

摘要

We investigate geometricity of operators for real-coded genetic algorithms. Geometric operator is a representation-independent generalization of the class of traditional mask-based operators for binary strings. It is defined as a function of the distance of the search space seen as a metric space. Although the real-coded representation allows for a very familiar notion of distance, namely the Euclidean distance, there are also other distances suiting it, such as Minkowski distances. Additionally, topological transformations of the real space give rise to further notions of distance. In this paper, we study geometric crossover operators associated with Minkowski spaces in a formal and general setting and show that some pre-existing genetic operators for the real-coded representation are geometric. Although geometric crossover operators defined in the plane are intuitive operators, in higher-dimensional spaces they are not trivial to understand and implement. We derive formally algorithms to implement these geometric crossover operators in the generic n-dimensional case. We compare the performance of the presented operators with existing ones on test functions which are commonly used in the literature.