A two-level hybrid evolutionary algorithm for modeling one-dimensional dynamic systems by higher-order ODE models

This paper presents a new algorithm for modeling one-dimensional (1-D) dynamic systems by higher-order ordinary differential equation (HODE) models instead of the ARMA models as used in traditional time series analysis. A two-level hybrid evolutionary modeling algorithm (THEMA) is used to approach the modeling problem of HODE´s for dynamic systems. The main idea of this modeling algorithm is to embed a genetic algorithm (GA) into genetic programming (GP), where GP is employed to optimize the structure of a model (the upper level), while a GA is employed to optimize the parameters of the model (the lower level). In the GA, we use a novel crossover operator based on a nonconvex linear combination of multiple parents which works efficiently and quickly in parameter optimization tasks. Two practical examples of time series are used to demonstrate the THEMA´s effectiveness and advantages