A supervised machine learning technique namely an Adaptive Multiple Objective (AMO) optimization algorithm is used to divide a continuous and deterministic design space into non-dominated Pareto frontier and dominated design points. The effect of the initial training data quantity, i.e., computational fluid dynamics (CFD) results, on the Pareto frontier and output parameter sensitivity is explored. The optimization study is performed on a subsonic small-scale cavity-stabilized combustor. A parametric geometry is created using CAD that is coupled with a meshing software. The latter automatically transfers meshes and boundary conditions to the solver, which is coupled with a post-processing tool. Steady, incompressible three-dimensional simulations are performed using a multi-phase realizable k-ε Reynolds-averaged Navier-Stokes (RANS) approach with an adiabatic flamelet progress variable (FPV). Scalable wall functions are used for modeling turbulence near the wall. For each CFD simulation four levels of adaptive mesh refinement (AMR) are utilized on the original cut-cell grid. The mesh is refined where the flow exhibits large progress variable curvature. There are fifteen geometrical input parameters and three output parameters, viz., a pattern factor proxy (maximum exit temperature), a combustion efficiency proxy (averaged exit temperature), and total pressure loss (TPL). The Pareto frontier and the input-to-output parameter sensitivities are reported for each meta-model simulation. For the investigated design space, three times the number of input parameters plus one (48) yields an optimization independent of the initial sampling. This conclusion is drawn by comparing the Pareto frontiers and global sensitivities. However, the latter provides a better metric. The relative influence of the input parameters on the outputs is assessed by using both a Spearman’s order-rank correlation approach as well as an active subspace analysis. In general, non-dominated design points exhibit persistent geometrical features such as offset opposed cavity forward and aft driver jet alignment. Larger cavities necessitate larger chutes and smaller outer liner jet diameters, whereas smaller cavities require smaller chutes and larger outer liner jet diameters. The fuel injector radial location varies, but can be located either radially inward or outward with respect to the forward dilution jet radial locations. For these non-dominated designs there is substantial burning inside and outside of the cavity. The downstream dilution jets quench the upstream hot gases.