In this study, a hybrid analytical-numerical framework is developed for the design and multi-objective optimization of two-ramp supersonic inlets under the shock-on-lip (SOL) condition at Mach 2.5. First, an analytical method based on oblique shock relations and the Oswatitsch criterion is employed to generate a reference optimal geometry. Subsequently, a comprehensive database of valid SOL-compliant geometries is constructed using oblique shock theory and geometric SOL constraints. A multi-objective optimization process is then conducted, considering two conflicting objectives: minimizing total ramp length and maximizing total pressure recovery. Results demonstrate that within the space of valid SOL configurations, total pressure recovery remains highly stable (variation of approximately 0.1%) despite a 28% change in total ramp length. This finding indicates that selecting the shortest-length configuration incurs virtually no significant aerodynamic penalty while offering substantial structural advantages, such as reduced weight and system complexity. Numerical validation via two-dimensional inviscid simulations confirms that the proposed approach is an efficient tool for rapid and design of supersonic inlets.