Selection of a robust experimental design for the effective modeling of nonlinear systems using Genetic Programming

The evolutionary approach of Genetic Programming (GP) has been applied extensively to model various non-linear systems. The distinct advantage of using GP is that prior assumptions for the selection of a model structure are not required. The GP automatically evolves the optimal model structure and its parameters that best describe the system characteristics. However, the evolution of an optimal model structure is highly dependent on the experimental designs used to sample the problem (system) domain and capture its characteristics. The literature reveals that very few researchers have studied the effect of various experimental designs on the performance of GP models and therefore the optimum choice of an experimental design is still unknown. This paper studies the effect of various experimental designs on the performance of GP models on two non-linear test functions. The objective of the paper is to identify the most robust (best) experimental design for effective modeling of non-linear test functions using GP. The analysis reveals that for the test function 1, the experimental design that gives best performance of GP models is response surface faced design and for test function 2, the best experimental design is 5-level full factorial design. Thus, the result concludes that the selection of the robust experimental design is a crucial preprocessing step for the effective modeling of non-linear systems using GP.