Approximating the Genetic Diversity of Populations in the Quasi-Equilibrium State

This paper analyzes an evolutionary algorithm in the quasi-equilibrium state, i.e., when the population of chromosomes fluctuates around a single peak of the fitness function. The analysis is aimed at approximating the genetic variance of the population when chromosomes are real-valued. The infinite population model is considered which allows the quasi-equilibrium state to be defined as the state when the density of chromosomes contained by the population remains unchanged over consecutive generations. This paper provides formulas for genetic diversity in the quasi-equilibrium state for fitness proportionate, tournament, and truncation selection types, with and without elitism, with Gaussian mutation, and with and without arithmetic crossover. The formulas are experimentally validated.