Multi-stage genetic programming: A new strategy to nonlinear system modeling

This paper presents a new multi-stage genetic programming (MSGP) strategy for modeling nonlinear systems. The proposed strategy is based on incorporating the individual effect of predictor variables and the interactions among them to provide more accurate simulations. According to the MSGP strategy, an efficient formulation for a problem comprises different terms. In the first stage of the MSGP-based analysis, the output variable is formulated in terms of an influencing variable. Thereafter, the error between the actual and the predicted value is formulated in terms of a new variable. Finally, the interaction term is derived by formulating the difference between the actual values and the values predicted by the individually developed terms. The capabilities of MSGP are illustrated by applying it to the formulation of different complex engineering problems. The problems analyzed herein include the following: (i) simulation of pH neutralization process, (ii) prediction of surface roughness in end milling, and (iii) classification of soil liquefaction conditions. The validity of the proposed strategy is confirmed by applying the derived models to the parts of the experimental results that were not included in the analyses. Further, the external validation of the models is verified using several statistical criteria recommended by other researchers. The MSGP-based solutions are capable of effectively simulating the nonlinear behavior of the investigated systems. The results of MSGP are found to be more accurate than those of standard GP and artificial neural network-based models.