Optimization procedures are performed using RANS models due to computational wall-clock time constraints. These trends are verified against selected LES counterpart simulations. The optimization study is performed on a subsonic small-scale cavity-stabilized combustor. Steady, compressible three-dimensional simulations are performed using a multi-phase Realizable k-ε Reynolds-averaged Navier-Stokes (RANS) approach or Dynamic Kinetic Energy Subgrid-scale LES. There are nineteen geometrical input parameters and four output parameters, viz., a pattern factor proxy (maximum exit temperature), a combustion efficiency proxy (averaged exit temperature), total pressure losses (TPL), and “melting” liner area. The RANS-based optimization with initial training sample of sixty design points leads to an optimum design point that dominates the baseline design, among other designs. The non-dominated design points release 57% of the heat inside the cavity in comparison to 43% from the baseline. Dominated combustors release as low as 23% of the heat in the cavity. The optimum, a dominated and the baseline design are compared with LES counterparts. The RANS predicted trends in terms of dominated and non-dominated design points were also confirmed by LES simulations, even though the output parameters quantitative values may differ. Discrepancies between RANS and LES appear more pronounced for the optimum design. This is attributed to the fact the LES permits pressure waves to escape the domain whereas RANS can only moderate pressure-induced disturbances. By allowing boundary-induced disturbances in the LES the flow field resembles that of RANS. Therefore, it is concluded that RANS and LES follow similar total pressure loss, pattern factor, and combustion efficiency trends as function of combustor design.