<p>The mechanical and geometric parameters of nonlinear fluid viscous dampers (NFVDs) play a crucial role in mitigating seismic demands by dissipating earthquake-induced energy. This study proposes an energy-based bi-objective optimization framework for the optimal design of NFVDs in chevron- and toggle-brace configurations. In the first stage, a comprehensive parametric analysis is conducted to investigate the coupled effects of damper properties, namely the damping coefficient (<i>C</i>_d) and velocity exponent (<i>α</i>), and toggle-brace geometry on the seismic energy balance of a steel moment-resisting frame. The results reveal a fundamentally non-monotonic relationship between <i>C</i>_d and damper energy dissipation, which is analytically explained through a critical elasticity condition linking velocity suppression and damping capacity, highlighting <i>α</i> as a key parameter governing optimality and robustness. In the second stage, a bi-objective optimization problem is formulated to maximize damper energy dissipation while minimizing cost, subject to constraints on hysteretic energy, drift, and supplemental damping ratio. A particle swarm optimization algorithm enhanced with a prioritized hierarchical decision-making scheme (PHD-PSO) is developed to solve the constrained problem without resorting to penalty functions or normalization. The results demonstrate that toggle-brace systems can achieve chevron-equivalent or superior seismic control with substantially lower damping coefficients due to geometric amplification, leading to markedly higher cost efficiency. However, under stringent drift constraints, the optimal toggle configuration naturally converges toward chevron-like behavior. Overall, the proposed framework enables efficient, physically interpretable, and economically optimized NFVD designs, which are further validated under recorded earthquake ground motions.</p>