Fractal Dimension of Trajectory as Invariant of Genetic Algorithms

Convergence properties of genetic algorithms are investigated. For them some measures are introduced. A classification procedure is proposed for genetic algorithms based on a conjecture: the entropy and the fractal dimension of trajectories produced by them are quantities that characterize the classes of the algorithms. The role of these quantities as invariants of the algorithm classes is presented. The present approach can form a new method in construction and adaptation of genetic algorithms and their optimization based on dynamical systems theory.