Multi-output DC-DC converters are widely used in compact power systems, but single-inductor dual-output (SISIDO) converters face critical challenges like cross-regulation and cross-coupling due to the shared inductor. This paper proposes a capacitor current ripple feedback (CCRF) control strategy for SISIDO buck converters to suppress self and cross-regulation and improve transient performance. A detailed small-signal model is systematically derived using state-space averaging, with compact expressions for control coefficients. Compensator parameters are optimized via Mountain Gazelle Optimization (MGO) for optimal dynamics. Sensitivity analysis shows parameter variations have negligible impact on regulation. The strategy is validated through MATLAB simulations, demonstrating superior load regulation, reduced cross-coupling, fast transient response, and robust performance under varying loads.