Multi-parent scanning crossover and genetic drift

Genetic drift is a well-known phenomenon from biology. Only recently has it gained attention in the field of evolutionary computation. In this article we argue that occurrence-based scanning causes a stronger than usual genetic drift. This is done in the context of a genetic algorithm based on the steady state model. To prove our claim we define three kinds of events: drift off events, drift back events, and neutral events, Drift off events constitute those events that increase the number of dominant alleles. Drift back events constitute those events that decrease the number of dominant alleles. Neutral events leave the numbers intact. We prove that in our context, with occurrence-based scanning, the probability of drift off events is always bigger than the probability of drift back events. Furthermore, we prove that this tendency to drift off amplifies itself, i.e., drifting off increases the probability of drifting off even further. Finally, we prove that the tendency to drift off gets stronger when the number of parents increases. For comparison we show that uniform scanning, another multi-parent crossover operator, does not influence genetic drift at all in this context.