I. Introduction
In general, large-scale physical systems are represented by complex higher-order models (HOM) in the real world. The complexity of such systems is a significant concern in analysis, synthesis, simulations, and controller design. Hence, a reduced-order model (ROM) is desired to preserve the essential characteristics of the original HOM. Some conventional model order reduction (MOR) methods are continued fraction expansion methods [1], Routh approximation [2], [10], Padé approximation [3], Hurwitz polynomial approximation [4], stability equation method (SEM) [5], balanced truncation [11], etc. The main disadvantage of the Padé approximation [3] is that occasionally, the approximants computed by this method become unstable as this method does not use any stability criterion. Therefore, stability preservation techniques (SPT) [4] are employed to overcome this issue by considering a specific stability criterion. Subsequently, several mixed methods [5] –[9] are proposed in which an SPT obtains the denominator polynomials of the ROM. At the same time, classical or optimization techniques are used to compute the coefficients of numerator polynomials in these mixed methods. Appiah [5] used the Hurwitz polynomial with Padé to obtain a ROM. Similarly, Singh et al. [6] utilized an improved Routh-Padé approach-based model reduction using optimization. Later, Parmar et al. [7]–[8] implemented Eigen spectrum analysis-based MOR techniques using the factor division [7] and Padé approach [8]. Another SPT is presented by Sikander et al. [9], where factor division and SEM are used. Pole clustering-based model reduction is also one of the SPT used in many works such as [15], [16]. Later, Prajapati et al. [18] proposed another method using balanced truncation [11] and factor division and showed a comparative analysis of various methods. A time-moment matching-based method [18] has been presented recently. However, this method fails to ensure the stability of a ROM due to the instability issue of Padé-based methods. Over the last few decades, many researchers have developed several nature-inspired metaheuristics optimization algorithms. Many of these algorithms are successfully implemented for MOR of LTI systems [19] –[24] such as Parmar et al. [19] presented SEM and genetic algorithm-based model reduction methods. Gupta et al. [20] developed the Eigen permutation and Jaya optimization-based technique to reduce LTI systems. The order reduction of HOM by these optimization algorithms is based on minimizing a specific performance criterion.