## 6 Conclusions  
By employing base isolators in the central pier of the benchmark bridge as a passive control strategy against seismic loadings, its stiffness and the load transmitted from the base to the superstructure decreased. On the other hand, the superstructure displacements increased. To control these displacements, SMA wires were utilized. However, adding the wires to the LRBs of the bridge increased the horizontal stiffness and, consequently, the deck acceleration and base shear. In order to get the best performance out of SMA wires, multi-objective optimization can be applied. Therefore, in this paper, the SMA wires were firstly optimized with the help of a multi-objective optimization algorithm named NSGA-II and the weighted sum method, and then added to the LRB isolators of the isolated benchmark bridge to reduce the residual deformations and displacements under the earthquakes available in the benchmark bridge package. In this way, the maximum mid-span displacement of the bridge and the maximum base shear force were simultaneously minimized. To assess the ability of this optimized system, the method was compared with the other three passive control approaches on the phase II of the benchmark bridge ([PERSON] et al. [26], [PERSON] et al. [27] and [PERSON] et al. [29]). Considering 16 main parameters, the results obtained by the nonlinear dynamic analysis of the benchmark structure under six different earthquakes were summarized. As regards far-field earthquakes, the suggested passive control device on average reduced the maximum mid-span displacement of the bridge and the maximum deformation of the base isolators by 43% and 45%, respectively. Also, the residual mid-span displacements of the bridge in the X- and Y-directions declined by 100% and 84.4%, respectively, on average. Nevertheless, using this device led to an average 16% and 46% rise in the base shear force and the maximum deck acceleration of the bridge, respectively. Regarding near-field earthquakes, by using this device, the maximum mid-span displacement and the maximum base isolator deformation reduced by 34% and 37%, respectively. On average, applying this system resulted in a 55% and 66% reduction in the residual mid-span displacements of the bridge in the X and Y directions, respectively. However, the SMA controller increased the base shear force and the maximum deck acceleration of the bridge by 23% and 124%, respectively, on average. As for comparing different passive devices, in general, using optimized SMA-LRB resulted in a drop of the mid-span displacement and bearing deformation more than the other measures. For example, it reduced the maximum bearing deformation by up to 58%, 31%, and 14% more than the non-linear dampers, negative stiffness device, and Cu-Al-Be dampers, respectively. It is undeniable that the base shear and mid-span acceleration of SRB are generally more than other controllers. However, the optimization kept them within bounds and still less than the figures before the isolation of the bridge. Figure 11: Graphical demonstration of the mid-span residual deformation before and after the SRBs in the (**a**) X and (**b**) Y directions. Comparing the two SMA passive controllers, i.e., Cu.D and SRB, revealed that the overall performance of the SRB is superior to the Cu.D. First of all, as said above, the SRB reduced the displacements more than the Cu.D. Secondly, the SRB increased the base shear of the bridge less than the Cu.D. Also, the manufacturing process of the Cu.D is more complicated and more expensive than implementing SMA wires in the LRBs of the bridge. Here, SMA wires were added to the existing LRBs of the bridge in a double-cross configuration. In future studies, various LRBs (different sizes and characteristics) with different wire configurations (straight and cross) need to be evaluated. Furthermore, in the benchmark bridge package, only six earthquake records were presented.