## 1 Introduction  
Water, fuels and chemicals are usually stored in large-scale tanks, which are often constructed in seismic-prone regions. In past earthquakes (e.g., Northridge 1994; Kobe 1995; etc. ), leakages and explosions were observed. In general, the main earthquake-related damages of liquid storage tanks are the following: (a) the \"elephant-foot\" buckling, (b) the \"diamond-shape\" buckling and (c) roof damage due to excessive liquid sloshing. Undoubtedly, such critical infrastructure should remain safe and functional even after a severe seismic event. Nonetheless, they behave quite differently to conventional structures (e.g., buildings, bridges, etc.) during an earthquake, due to the hydrodynamic interaction of their walls with their liquid content. [PERSON] [1] developed a mechanical analogue to simulate the hydrodynamic response of the liquid-tank system by decoupling it from two components: (i) the lower part of the liquid content that moves together with the tank walls, the so-called impulsive component, and (ii) the upper part of the liquid content that moves independently and causes sloshing, i.e., the convective component. Subsequent studies (by [PERSON] et al. [2]; [PERSON] [3]; among others) have proven that the global tank response is mainly governed by the impulsive component of the liquid content. Consequently, the convective component can be neglected, as it is related to high periods (e.g., >6 s for the examined tank in the present investigation), that are considerably higher compared to the fundamental period of the tank-liquid system (e.g., \(\approx\)1.5 s for the examined isolated tank, while it is <0.2 s for the same tank for fixed-base conditions). In order to diminish the potential detrimental effects of the ground motions on large and/or important structures and non-structural elements (e.g., status, sensitive equipment, etc. ), several base-isolation schemes have been frequently applied in engineering practice [4]. The main goal of all base-isolation schemes is to \"decouple\" the response of the superstructure from the imposed ground shaking via suitable devices with low horizontal and high vertical stiffness, which is necessary in order to carry the structural weight. In this manner, the dynamic distress of the tank is considerably reduced, while the displacements are increased due to the increased flexibility of the isolators. Such base-isolated tanks with quite large dimensions have been constructed in many countries. Many researchers have applied various optimization formulations and techniques to design isolators that exhibit an optimal dynamic performance. Several studies have investigated the performance of frictional bearings utilizing an optimization formulation. [PERSON] [5] presented the optimization of friction coefficient of a sliding system to minimize the accelerations of a base-isolated structure under seismic excitations. It was reported that the damping ratios and the periods of the isolation system and the structure, the ratio of base to superstructure masses, as well as the frequency content and the intensity of seismic excitations had a significant impact on the results. Subsequently, [PERSON] [6] investigated the behavior of buildings isolated via single friction pendulum bearings (SFPB) under near-fault excitations. The objective was the minimization of sliding displacements and top accelerations, while the resulting optimal coefficient of friction values were between 0.05 to 0.15. [PERSON] [7] improved the performance of friction-based isolators by developing a Pareto-type optimization formulation with conflicting objective functions. It was found that the optimized design parameters are taken from a relatively narrow range of values. A non-dominated sorting genetic algorithm (NSGA-II) was applied by [PERSON] et al. [8] to perform optimization on SFPB isolators installed at a masonry house in Chile. It was found that SFPB isolators reduced the superstructure demands. [PERSON] et al.