It´s all the same to me: revisiting rank-based probabilities and tournaments

One of the defining operations of genetic algorithms is selection: choosing chromesomes from the population to generate offspring via crossover or mutation. Researchers have described many selection algorithms, including schemes that apply probabilities based on chromosomes´ ranks in the population and that simulate tournaments among chromosomes. The paper investigates two rank based assignments of probabilities: linear normalization and exponential normalization, and two tournament selection schemes: 2-tournament selection without replacement and k-tournament selection with replacement. It makes explicit the probabilities that each associates with the population´s chromosomes; demonstrates, following other researchers but using elementary arguments based on these probabilities, the equivalence of linear normalization with 2-tournament selection and of exponential normalization with k-tournament selection; and argues for the use of tournament selection rather than the explicit assignment of rank based probabilities whenever possible