Evolutionary Modeling of Systems of Ordinary Differential Equations with Genetic Programming

This paper describes an approach to the evolutionary modeling problem of ordinary differential equations including systems of ordinary differential equations and higher-order differential equations. Hybrid evolutionary modeling algorithms are presented to implement the automatic modeling of one- and multi-dimensional dynamic systems respectively. The main idea of the method is to embed a genetic algorithm in genetic programming where the latter is employed to discover and optimize the structure of a model, while the former is employed to optimize its parameters. A number of practical examples are used to demonstrate the effectiveness of the approach. Experimental results show that the algorithm has some advantages over most available modeling methods.