This taking up of the entire population by one extremely fit solution is known as premature convergence and is an undesirable condition in a GA. Maintaining good diversity in the population is extremely crucial for the success of a GA. However, care should be taken to prevent one extremely fit solution from taking over the entire population in a few generations, as this leads to the solutions being close to one another in the solution space thereby leading to a loss of diversity. Parent selection is very crucial to the convergence rate of the GA as good parents drive individuals to a better and fitter solutions.
Parent Selection is the process of selecting parents which mate and recombine to create off-springs for the next generation.