COMPUTERS and SIMULATION in MODERN SCIENCE Volume IV

Genetic algorithms are random heuristic search algorithms which mimic biological evolution and molecular genetics in simplified form. These algorithms can be theoretically described by an infinite population model with the help of a deterministic dynamical system by which the stochastic population trajectory is characterized using a deterministic heuristic function and its fixed points. For practical problem sizes the determination of the fixed points is unfeasible even for the simple genetic algorithm with fitness-proportional selection, crossover and bitwise mutation. The simple genetic algorithm with α-selection allows the analytical calculation of the unique fixed point of the corresponding intrinsic system model. In this paper, an overview of the theory of the simple genetic algorithm with α-selection, uniform crossover and bitwise mutation is given and experimental results are presented showing a close agreement to the theoretical predictions.