An analysis of crossover´s effect in genetic algorithms

The crossover operation is characteristic of genetic algorithms (GAs). This paper analyzes the crossover effect in GAs. We start with two bits, that is the minimum chromosome length to crossover. We compare one operator GAs, using only selection, and two operators GAs by selection and crossover with respect to the expected quality and speed of the convergence. First, we analyse the case of two individuals, that is the minimum population size, by a Markov chain. We show the boundary in the fitness assignment cube where crossover improves the absorption probability to the optimum. We also show that crossover always speeds up convergence. Second, we analyse the larger population case by numerically solving the difference equations. We show a boundary where the crossover speeds up convergence. Normal medium sized GAs can be positioned between these two extremes