The design of acoustic liners with complex cavities for a wide frequency range of attenuation using numerical method is investigated in this paper. Three novel liner concepts are presented, demonstrating predicted improvements in broadband sound absorption when compared with that for conventional designs. The liners include a slanted septum core, a slanted septum core with varying percentage open area, and a MultiFOCAL concept. A finite element model of a normal incidence impedance tube is developed using COMSOL Multiphysics modeling software to predict the acoustic properties (resistance and reactance) of liners at medium and high sound pressure levels, and to study the impact of variations in the liner design parameters. The impedance tube finite element model incorporates non-linear semi-empirical impedance equations, validated by comparing numerical results with measurements performed on a single-degree-of-freedom liner, with a perforated face sheet, at high sound pressure level. The design variables of the novel liner concepts are optimized using a hybrid automated optimisation procedure. The low-frequency optimum slanted septum core concept with an open area of 4.5% for the face sheet and 18% for the short slanted septum is predicted to have an absorption level of at least 14 dB in the frequency range of 400–1000 Hz for normally incident pure tone excitations at 150 dB. The slanted septum core concept with varying percentage open area, with broadband optimum design variables, is predicted to have good broadband sound absorption levels of at least 10 dB in the frequency range of 570–3800 Hz. Finally, the MultiFOCAL liner concept with optimised percentage open areas is predicted to have an excellent broadband sound absorption levels of at least 14 dB, for pure tone excitations at 150 dB, in the frequency range of 900–5300 Hz. This work will be followed by optimisation of the face sheet geometries of these novel liner designs in order to maximise lined duct attenuation for aircraft engine applications.