Gender Supremacy: A theoretical demonstration of gender genetic algorithm's superiority over standard genetic algorithm using schema theory

Genetic algorithm (GA) is a highly popular derivative-free optimization method that is widely used in real-world tasks. There are numerous studies on GA modifications aimed at improving its search efficiency. Gender GA (GGA) is one of them. GGA divides a population into two parts (genders) with high and low mutation rates, and constrains the crossover of individuals of the same gender.

Typically, all new modifications of GGA are validated with computational experiments on a list of problems. This provides practical knowledge about the performance of new modifications, but not a general understanding of the effectiveness of gender introduction. In this study, we consider binary-coded GGA using Holand’s schema theory. Comparison of the growth values for different schemata orders o(H) shows GGA's superiority over standard GA. This result does not require problem specification and represents theoretical evidence of GGA's supremacy over GA.

Another interesting result of this study lies in the field of biology: the observed superiority of GGA over GA may indicate an advantage of genderized species over non-genderized species. Along with the Red Queen hypothesis, this can be treated as an additional explanation of the advantage of sexual reproduction. However, since GGA represents a highly simplified version of the biological evolution process of genderized species, it should be treated with some skepticism, and requires further investigation.