Four-Group Equation of Genetic Algorithm

Abstract

A nonlinear differential equation system of only four variables is proposed to describe the time-dependent appearance probabilities of the best-adapted gene and the other three mutant groups in the genetic algorithm. All the strings are classified into four groups according to the Hamming distance. Each group has the temporal-dependent frequency distribution plotted against the fitness-value, which is called the fitness-probability landscape. The present simple model for the genetic algorithm is an analogical one such as the Lorentz model for the thermal convection flow. Several types of evolutionary routes are predicted by varying three metabolic-rate-controlling parameters and the problem. The predictions are confirmed by performing numerical calculations with a concrete genetic algorithm. Artificial constants in the genetic algorithm can be optimized by using the present theoretical approach before the trial of evolution is performed.