Theoretical analysis on an inversion phenomenon of convergence velocity in a real-coded GA

The aims of this paper are to analyze an inversion phenomenon theoretically and discussion on appropriateness of combination of a crossover operator and a selection model. In the previous study, the author designed a crossover operator that worked well on various kinds of objective functions. One of the features of the objective functions is "the optimum exists near a boundary much more than the other". On such objective functions, with recommended selection model, the proposed crossover operator set with an appropriate parameter has shown the fastest convergence speed. However, with another selection model, its convergence speed has been the slowest. In order to understand this inversion phenomenon, a theoretical analysis quantified the selection pressures of the selection models and estimated the expected positions of the center of gravity of the population. The theoretical results corresponded to empirical verifications and successfully explained. Finally, a guideline for designing RCGAs was obtained.