Theoretical analysis of selection operator in Genetic Algorithms

Genetic algorithms (GAs) have gathered much attention by researchers and practitioners because of successful results in many real-world optimization problems [4], [5], [6]. However, to our knowledge, the working mechanism of GAs, in particular dynamics of GAs, is still unclear and should be investigated. Since we believe that the theoretical analysis of dynamics will help us not only to understand the working mechanism of GAs but also to develop more efficient algorithms, we proposed the theoretical framework to analyze the dynamics of GAs in [14]. Since we formulated only crossover and mutation in [14], we formulate selection operator in this paper as an extension of our previous paper. Based on the proposed theoretical framework, this paper analyzes the dynamics of selection and derives several theorems.