Optimization of isolation system involves a trade-off between the isolation efficiency and isolator displacement to ensure optimal performance. Quite often, the latter aspect is overruled, even though, large isolator displacements are known to be linked with adverse consequences. A class of smart material referred as Shape Memory Alloy (SMA) has recently been proposed to supplement the conventional isolation bearings that is shown to facilitate such trade-off, owing to its Superelastic property. Recent usage of SMA in supplementing rubber bearing to isolate highway bridge is notable. Presently, the SMA is employed in conjunction with the Lead Rubber Bearing (LRB) (referred as SMA-LRB), isolating multi-storied building frame. It is demonstrated that SMA-LRB largely reduces the isolator displacement with very little sacrifice in the isolation efficiency while compared with the conventional LRB. The nonlinear random vibration analysis in conjunction with stochastic linearization of SMA behavior demonstrate that optimal combination of the SMA and LRB characteristics strengths are essential to ensure such performance. This includes minimizing the isolator displacement as well as maximizing the isolation efficiency, dealt in a framework of bi-objective optimization. Robustness of the optimal design is verified through parametric studies concerning the anticipated variations in system parameters and seismic loading. (C) 2015 Elsevier Ltd. All rights reserved.