Multiobjective model structure optimization using hybrid differential evolution for multivariable dynamic system modeling

Abstract

Most real engineering systems are multivariable systems and multiobjectives in nature, especially in a complex dynamic system. The ultimate objective of dynamic system modeling is to obtain parsimonious and adequate model, where the predictive error and model complexity need to be optimized and satisfied simultaneously. This study attempts to establish the needs of a multiobjective optimization algorithm by comparing it with a single-objective of the multivariable optimization algorithm. Two different types of optimization techniques are used: (1) elitist the non-dominated sorting genetic algorithm (NSGA-II) for multiobjective optimization and (2) the modified genetic algorithm (MGA) for single-objective optimization. The results showed that advantage of the multiobjective optimization algorithm compared with the single objective optimization algorithm in developing an adequate and parsimonious model for a discrete-time multivariable dynamics system. A new algorithm based on a multiobjective optimization algorithm for model structure selection is proposed namely multivariable multiobjective optimization using hybrid differential evolution (MOHDE). The proposed algorithm was compared with NSGA-II for model selection in dynamic system modeling of multivariable optimization. The study involved simulated and real systems data for comparison in terms of model predictive accuracy and model complexity. The case studies for real systems were considered in this study for investigating the effectiveness of the multivariable proposed algorithm namely Reference Evapotranspiration (ETo) for MISO systems, offshore structure response for SIMO systems and CD-player arm for MIMO systems. The results showed that the proposed algorithm is capable to produce a good and adequate model with a minimal number of terms and a good predictive accuracy with lower error (less than 1%) on average for all study cases where the result shows that MOHDE outperformed NSGA-II.