Meta-heuristic algorithm based system identification and multi-criteria decision making approaches in time delay systems

In control of feedback systems, mathematically accurate modeling of system components is of critical importance for ensuring stability and desired dynamic performance. However, as the number of system components increases, the modeling process becomes increasingly complex and time-consuming. In such cases, black-box system identification methods based on time-delayed transfer functions provide a practical and effective solution by utilizing only input–output data. In this study, Harris Hawk Optimization (HHO) and Electromagnetic Field Optimizer (EFO) algorithms are proposed to solve the black-box system identification problem. The performances of both algorithms are comparatively evaluated against other meta-heuristic algorithms. Experimental results indicate the presence of inherent system delays; therefore, a time-delayed model structure is adopted. The optimization problem is formulated as the estimation of model coefficients that minimize the error between measured and estimated system responses. Initial performance evaluation based on the coefficient of determination shows that the HHO algorithm achieves the highest accuracy, reaching an R2 value of 0.989. However, the results also demonstrate that relying solely on a single performance indicator may lead to misleading conclusions. Consequently, three different performance metrics—R2, rise time, and solution time are simultaneously considered, and the algorithms are evaluated using multi-criteria decision-making (MCDM) methods, namely TOPSIS, MABAC, COMET, and SPOTIS. According to the MCDM-based rankings, the EFO algorithm consistently outperforms the others by providing a more balanced trade-off between accuracy, dynamic response, and computational efficiency. Notably, although HHO exhibits superior accuracy, it does not rank among the top-performing algorithms when multiple criteria are considered. These findings highlight the importance of integrating meta-heuristic algorithms with MCDM approaches to achieve more reliable and practically applicable system identification results, particularly for time-delayed systems.