Polynomial NARX model structure optimization using multi-objective genetic algorithm

Abstract

Model structure selection is an important step in system identification which involves the selection of variables and terms of a model. The important issue is choosing a compact model representation where only significant terms are selected among all the possible ones beside good performance. This research explores the use of multi-objective optimization to minimize the complexity of a model structure and its predictive error simultaneously. The model structure representation is a polynomial non-linear auto- regressive with exogenous input model. A new modified elitist non-dominated sorting genetic algorithm using clustered crowding distance (CCD) is proposed to find the exact model among non-dominated solutions, using some simulated examples which generate data set by mathematical equations. Simulation results demonstrated that the proposed algorithm can find the correct model with exact terms and values in all cases of problem. Furthermore, the effectiveness of the proposed algorithm is also studied by applying to the real process data sets, and the final model can be chosen from a set of non-dominated solutions referred as Pareto optimal front. The results show that the proposed clustered CD has better performance compared with the basic CD method.