Genetic algorithms: Biologically inspired, fast-converging optimization

As you can see, beyond the details and the actual exact probability, the chances of any individual (but the first) are decreasing exponentially with k (while polynomially with m). It goes without saying that we need to apply tournament selection twice to get the pair of parents we need to generate a single element in the new population. Roulette wheel selection is definitely more complicated to implement than tournament selection, but the high-level idea is the same: higher-fitness individuals must have more chances to be selected. As we have seen, in tournament selection the probability that an element with low fitness is chosen decreases polynomially with the rank of the element (its position in the list of organisms sorted by fitness); in particular, since the probability will be O([(n-m)/n]k) the decrease will be super-linear, because k is certainly greater than 1. If, instead, we would like for lower-fitness elements to get a real chance of being selected, we could resort to a fairer selection method.