An adaption of the schema theorem to various crossover and mutation operators for a music segmentation problem

Abstract

The schema theorem provides theoretical background for the effectiveness of genetic algorithms and serves as a formal model to explain their success. It describes the functionality of genetic algorithms under very restrictive limitations of a canonical genetic algorithm which applies a binary alphabet, individuals of equal length, fitness-proportional selection, single-point crossover, and gene-wise mutation. Applications of genetic algorithms, however, are often based on noncanonical variations and, therefore, are not verified by the theory of the traditional theorem. This paper describes the adaption of the theorem for various other crossover and mutation operators focusing on the application of genetic algorithms to a music segmentation problem.