Specific modification of a GPA-ES evolutionary system suitable for deterministic chaos regression

The paper deals with symbolic regression of deterministic chaos systems using a GPA-ES system. A Lorenz attractor, Rössler attractor, Rabinovich–Fabrikant equations and a van der Pol oscillator are used as examples of deterministic chaos systems to demonstrate significant differences in the efficiency of the symbolic regression of systems described by equations of similar complexity. Within the paper, the source of this behavior is identified in presence of structures which are hard to be discovered during the evolutionary process due to the low probability of their occurrence in the initial population and by the low chance to produce them by standard evolutionary operators given by small probability to form them in a single step and low fitness function magnitudes of inter-steps when GPA tries to form them in more steps. This low magnitude of fitness function for particular solutions tends to eliminate them, thus increasing the number of needed evolutionary steps. As the solution of identified problems, modification of terminals and related crossover and mutation operators are suggested.