Comparison between multi-objective and single-objective optimization for the modeling of dynamic systems

Abstract

Modeling input–output data representing a dynamic system is a challenging task when multiple objectives are involved. The developed model needs to be parsimonious yet still adequate. To achieve these goals, two objective functions, i.e. optimum structure and minimum predictive error, need to be satisfied. Most works in system identification only consider one objective function, i.e. minimum predictive error, and the model structure is obtained by trial and error. This paper attempts to establish the needs of a multi-objective optimization algorithm by comparing it with a single-objective optimization algorithm. In this study, two different types of optimization algorithms are used to model a discrete-time system. These are an elitist non-dominated sorting genetic algorithm for multi-objective optimization and a modified genetic algorithm for single-objective optimization. Simulated and real systems data are studied for comparison in terms of model predictive accuracy and model complexity. The results show the advantage of the multi-objective optimization algorithm compared with the single-objective optimization algorithm in developing an adequate and parsimonious model for a discrete-time system.