Linear selection

In most forms of selection, when multiple individuals are needed for an operation, these are drawn independently from the population. So, for example, in the case of crossover, the probability of a particular pair of parents being selected is given by the product of the selection probabilities of each parent. In this paper we investigate a form of selection where pairs of parents are not selected independently. We show that a particular form of dependent selection, linear selection, leads a genetic algorithm with homologous crossover to become very similar to a genetic algorithm with standard (independent) selection and headless chicken crossover, i.e., it turns crossover into a type of mutation. In the paper we analyse this form of selection theoretically, and we compare it to ordinary selection with crossover and headless chicken crossover in real runs.