## 1 Introduction
### Optimization of Seismic Isolation Systems  
Seismic isolation systems are used in specialized structures, so simple methods are not enough for their design. Although the equivalent lateral load method suggested in the seismic codes suggests modeling methods for seismic isolation systems, structural responses are not taken into account during the design phase. Significantly more iterations are required in performance-based design when seismic-isolated structural reactions are taken into consideration. However, even a large number of iterations is not sufficient to determine the most appropriate parameters in the nonlinear design of seismic isolation systems. Because the designer changes the isolation parameters, the structure responses change unpredictably. For this reason, it is preferred by researchers to use advanced meta-heuristic algorithms to optimize the isolation parameters. Meta-heuristic methods maximize or minimize the objective function within certain constraints. The seismic isolation problem is also a complete optimization problem in terms of finding the isolation parameters that optimize the structure responses within the isolator constraints. Different objective functions and meta-heuristic methods have been used by researchers aiming to optimize seismic isolation parameters. An early study in seismic isolation optimization by [PERSON] and [PERSON] aimed to simultaneously minimize the displacement of the building's top floor and the base isolation system. In the study, where the genetic algorithm is used, variable parameters are selected as the mass, stiffness, and damping ratio [15]. [PERSON] et al. optimized the isolation system in a four-span bridge structure with a micro-genetic algorithm. They defined the mechanical properties and prices of eight isolator types. They determined the type and number of isolators by minimizing the cost [16]. [PERSON] et al. optimized seismic isolation systems using the harmony algorithm. In their study, they classified real earthquake data as near- and far-field earthquakes. The example they solved was a four-story building using seismic isolators. They determined the structure type, earthquake data, and displacement and damping ratio limits in the building and optimized the isolation system parameters [17]. In another study, single, double, and triple friction pendulum bearing parameters were optimized using swarm intelligence. In the study, where liquid storage tanks were modelled as superstructures, the aim was to minimize the eccentricity of the isolation system by limiting the damping ratio and period [18]. [PERSON] et al. optimized friction-based isolators in liquid storage tanks via a cuckoo search algorithm. They investigated the fragility curves of the isolators and the accelerations of the superstructure [19]. Another study employed the gray wolf optimizer (GWO), whale optimization (WOA), and crowd search (CSA) to try to identify the best values for period and \(F_{Q}/W\) ratio. The ratio of peak roof acceleration to peak ground acceleration was chosen as the objective function in the study, which used a four-story shear structure, and isolator displacement was chosen as the limit [20]. [PERSON] et al. investigated the use of meta-heuristic algorithms, including Jaya algorithms (JA), teaching learning-based optimization (TLBO), floral pollination algorithm (FPA), and harmony search (HS), to optimize the damping ratio and period of low-, medium-, and high-damping base isolators. Taking into consideration soil-structure interaction on three distinct soil types, the aim was to minimize the structure's acceleration and displacement [21]. In a recent study, inter-story drift, top-story drift, strength, displacement, and the connection geometry of beams and columns were selected as limits, aiming to select optimum isolators. Using artificial bee colony, crow search, and Archimedes optimization algorithms, the dimensions of the steel elements were used as the objective function, and the minimum structure weight was determined [22].