Modeling Systems of Ordinary Differential Equations Using Immune Based Gene Expression Programming

This paper aims to model system of ordinary differential equations by using a new hybrid gene expression programming algorithm. Gene expression programming is a recently developed evolutionary computation method for model learning and knowledge discovery. The hybrid algorithm combined immune clonal selection algorithm and memetic algorithm with gene expression programming to find not only the structure of system of differential equations but also optimize its constant parameters. The idea of immune clone principle is incorporated into the evolution process to enhance the diversity of population and the memetic algorithm is introduced to improve the ability of local search. Experiments on benchmark problems have shown that the hybrid approach is able to provide highly competitive results compared with that of conventional genetic programming applied to this problem.