This work presents an on-design component-level multiple-objective optimization of a small-scaled uncooled cavity-stabilized combustor. Optimization is performed at the maximum power condition of the engine thermodynamic cycle. The CFD simulations are managed by a supervised machine learning algorithm to divide a continuous and deterministic design space into non-dominated Pareto frontier and dominated design points. Steady, compressible three-dimensional simulations are performed using a multi-phase Realizable k-? RANS and non-adiabatic FPV combustion model. Conjugate heat transfer through the combustor liner is also considered. There are fifteen geometrical input parameters and four objective functions viz., maximization of combustion efficiency, and minimization of total pressure losses, pattern factor, and critical liner area factor. The baseline combustor design is based on engineering guidelines developed over the past two decades. The small-scale baseline design performs remarkably well. Direct optimization calculations are performed on this baseline design. In terms of Pareto optimality, the baseline design remains in the Pareto frontier throughout the optimization. However, the optimization calculations show improvement from an initial design point population to later iteration design points. The optimization calculations report other non-dominated designs in the Pareto frontier. The Euclidean distance from design points to the utopic point is used to select a "best" and "worst" design point for future fabrication and experimentation. The methodology to perform CFD optimization calculations of a small-scale uncooled combustor is expected to be useful for guiding the design and development of future gas turbine combustors.