<p>The performance of cable-stayed bridges is drastically conditioned by the design of their cable-supporting system. Finding the optimal combination of cross-sectional areas and prestressing forces for a given cable-supporting system configuration is crucial to ensure safety and cost-effectiveness. Despite the clear benefits of structural optimization techniques for this goal, their implementation in the industry and the research realm when addressing natural hazards is quite limited due to their high computational demands and implementation challenges. This study proposes and compares four different optimization strategies aiming at reducing the computational burden, laying the foundation for their effective formulation and implementation. The first strategy is a traditional nested approach, which considers all cable cross-section areas as design variables and calculates the prestress values in each evaluation by solving a system of linear equations to achieve zero dead load displacement. The second method, simultaneous optimization, involves both area and prestress values as design variables, while solving the zero-displacement constraint by imposing dead load displacement constraints. Moreover, two new sequential optimization methods divide the optimization into two stages: area optimization and prestress values calculation. This second phase is solved by a standalone optimization process, or by solving the zero-displacement system of equations. Comparisons conducted using three application examples revealed the advantages and limitations of each method, demonstrating the strong reliability of simultaneous optimization and the potential of the sequential method to significantly alleviate the computational burden in multivariate design problems.</p>