_Article_  
**Multi-Objective Optimization of Three Different**  
**SMA-LRBs for Seismic Protection of a Benchmark**  
**Highway Bridge against Real and Synthetic**  
**Ground Motions**  
**[PERSON] 1,*\({}^{\text{\text{\textcircled{\textcircled{\textcircled{\textcircled{\textcircled{\textcircled{\text{\textcircled{\text{\text{\text{\text{\text{\text{\text{\  
the structure [7]. In the current design practice, the bridge superstructures are mainly designed to stay in their elastic region during earthquakes, and foundation failure is hard to assess. Therefore, only the bridge substructure is allowed to dissipate input energy through inelastic deformations. However, unlike buildings, bridges lack redundancy as a result of their simple structural configurations. Due to the lack of redundancy, bridges cannot provide adequate ductility demand enforced by large earthquakes [8]. To tackle this problem, over the past decades, researchers have focused on employing vibration control strategies to either reduce the earthquake force acting on a structure or to absorb the seismic energy [9]. Amongst various control strategies, base isolation is a prevalent technique for mitigating seismic response and is applied in bridges worldwide. Seismic isolation aims to lengthen the natural period of a structure in order to reduce the applied seismic loads and provide additional damping capacity to the structure. Different types of isolation systems have been suggested and developed for various structures. Commonly adopted systems are rubber bearing (RB), lead rubber bearing (LRB), high damping rubber bearing (HDRB), friction pendulum (FP), and resilient friction bearing, amongst which LRB is the most broadly used device [10]. However, base isolations have several downsides. The major one is the occurrence of the large displacements under strong ground excitations, which may result in the bounding of adjacent parts or even unseating, instability due to large deformation, unrecovered residual deformation, and an urgent need for the replacement of bearings after strong earthquakes [11]. A novel way to minimize excessive displacements is to employ intelligent materials, such as shape memory alloys (SMAs), to produce additional damping and re-centering ability. SMAs are intelligent materials with extraordinary properties. The eminent properties of these materials are super-elasticity and shape memory effect [12]. In the super-elastic behavior, the strain due to loads can be recovered entirely after unloading. However, in the shape memory effect, the initial shape can be returned by heating [13]. Since [PERSON] first found Nitinol in 1963, various types of SMAs have been presented [14]. The most common ones are nitinol-based, copper-based [15], and iron-based [16] SMAs. Recently, an iron-based alloy (i.e., FeNiCoAlTaB) was found which is able to hold 13.5% super-elastic strain [16]. In the last two decades, many researchers have used SMAs to improve the seismic performance of base isolators due to their high damping capacity, erosion resistance, fatigue strength, and high level of super-elastic strain. [PERSON] et al. [17] took advantage of two different systems, including a rubber bearing with an SMA bar damper and a lead core rubber bearing (LRB) with lateral bracing named NZ device. By comparing these systems, it was observed that the first system has more damping capacity, and because of using SMA, this system was able to recover its deformation. However, the force applied to the base isolator with SMA was three times more than the other one. To control the instability and residual deformation in a three-span continuous highway bridge, [PERSON] et al. [18] took advantage of SMA wires, which were wrapped around an elastomeric bearing. Findings proved that the rubber bearing with Nitinol shape memory alloy was able to decrease the deck displacement, and no residual displacement was observed.