## 8 Conclusions  
The present study aims to improve the dynamic response of isolated tanks in a cost-efficient manner by optimizing both the isolator layout and critical parameters, i.e., the friction coefficient and radius of curvature of each (single or multiple) sliding surface. According to the review of the relevant literature, there is no relevant study that has focused on the combined optimization of both the key parameters (i.e., sizing optimization) and the layout (i.e., optimal placement) of the isolators installed at the base of buildings or tanks. For this purpose, the constrained optimization of SFPB and TFPB isolators installed at the base of liquid storage tanks has been investigated herein. More specifically, the dynamic performance of tanks isolated by SFPB or TFPB has been optimized firstly with respect to the properties of the isolators and then together with their optimal placement at tank's base. For this purpose, the seismic vulnerability--in terms of isolators displacements and superstructure accelerations--has been examined for each optimized configuration. In order to achieve an optimal balance between computational accuracy and efficiency, an efficient surrogate model has been used for the realistic representation of the hydrodynamic response of the tank. According to the presented results, the main findings of this preliminary investigation can be summarized as follows:  
1. The dual optimization approach (SFPB3, TFPB3) leads to a substantially more cost-efficient design for both isolator types. More specifically, SFPB3 and TFPB3 resulted in 39 and 36 isolators, respectively, for the examined squat cylindrical tank. On the other hand, the conventional design (SFPB1, TFPB1) and the single optimization (SFPB2, TFPB2) procedures required 60 isolators, regardless of the bearing type. Moreover, despite this significant reduction in the required isolators, the differences in the isolators' properties--and cost--are small compared to full configurations. Thus, the total cost of the isolation system in dual schemes is much less for both bearing types. 2. Regarding the fragility curves of the isolators, marginal differences were noticed only in the case of TFPB, while for SFPB, the results were identical to the conservative design approach for both single and dual optimization formulations. Figure 10: Base accelerations of the storage tank for: (**a**) SFPB and (**b**) TFPB isolation schemes. 3. A significant reduction in accelerations transmitted to the superstructure was observed for all isolation schemes, especially in the case of TFPB, which is slightly increased in the case of dual optimization configurations and extreme PGA levels. 4. For both isolator types, the single (i.e., only sizing) optimization converged faster than the dual formulations due to the additional complexity related to the optimal placement of the bearings. Consequently, by applying the proposed optimization methodology, optimal configurations with reduced number of isolators could be used in large-scale projects, leading to a more cost-effective design of base-isolated structures. Certainly, further investigation must be performed, including a more detailed cost analysis regarding the topology of the isolators (grid type and/or non-constant locations) and their sizing parameters. In addition, the optimization problem could be formulated with discrete design variables and/or by grouping isolators with similar properties, since such alternative optimized designs would be more viable from a practical point of view. Furthermore, a multi-objective optimization formulation of hybrid isolation systems--consisting of friction-based isolators and supplemental dampers [64], tuned mass dampers [65; 66] or semi-active/active control devices [67]--can also be examined as an extension of this work. Conceptualization, A.T. and Y.T. ; methodology, A.T., A.S. and Y.T. ; software, A.T. and A.S.; validation, A.T. and A.S.; formal analysis, A.T.; investigation, A.T., A.S. and Y.T. ; resources, A.T. and Y.T.