Multi-objective optimization method for hybrid isolation systems using explicit seismic response prediction

In highly seismic regions, a hybrid isolation system integrating isolators and viscous dampers can achieve both isolation efficiency and displacement control. However, the quantitative design of damper parameters lacks theoretical guidance. To address this bottleneck, this study proposes a multi-objective optimization design method balancing isolation-layer displacement and total shear control. First, based on the energy balance equation, explicit mappings of the displacement response ratio and shear response ratio versus the added damping ratio are derived. These mappings allow direct estimation of structural responses. Then, a design framework based on minimizing a weighted sum function is established, from which the optimal added damping ratio can be determined according to engineering needs. Case validation demonstrates that the explicit formulas yield predictions within a 20% deviation compared with time-history analysis results, meeting the accuracy requirements of preliminary design. Unlike data-driven approaches that require extensive training datasets and iterative searches, the proposed explicit formulas enable physics-consistent response estimation without any training phase. This method offers a practical tool for the preliminary design of low-to-medium-rise isolated structures and lays a methodological foundation for the analytical optimization design of complex isolation systems.