Noise can be controlled in naturally ventilated indoor spaces using sound-absorbing panels or ventilated sound barriers. The former has thickness limitations while the latter can be as thick as the exterior wall but requires a specific opening size for air passage. This paper presents a design approach that utilizes the differential evolution algorithm to derive a broadband low-frequency resonator panel. The panels consist of arrays of cells with a central waveguide connecting four Helmholtz Resonators (HRs), and the other end of this waveguide is either closed or open to derive two functionally different resonator panels: a rigidly backed absorption panel and a ventilated sound barrier panel. Three optimization methods are discussed to obtain optimal panel designs: absorption-optimized, impedance-optimized, and phase-optimized. The phase optimization approach is a novel method for panel designs and proved to achieve results comparable to the other two standard approaches. The absorption performance and the transmission loss for rigid-backed and ventilated panels, respectively, are analytically predicted and numerically verified.