Runtime Analysis of Non-Elitist Evolutionary Algorithms with Fitness-Proportionate Selection on Royal Road Functions

It has been shown before that some results from the theory of evolutionary algorithms (EAs) may be used for the analysis of population dynamics in biology. In the present paper, we study the EAs without elite individuals, where the fitness-proportionate selection is used, on the class of Royal Road fitness functions. The behavior of EAs with these fitness functions may be considered as a model of population dynamics in the case of fitness landscape with several neutrality regions. We obtain lower and upper bounds on the expected time of evolving the fittest possible genotype for the Royal Road fitness function. It is expected the obtained results to be useful in development of modeling tools for biological populations.