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Abstract Combustor turbulence in a gas turbine engine greatly influences the efficiency of the downstream high pressure turbine stage. Here we use a multi-fidelity computational optimization methodology to modify the geometry of a non-reacting combustor simulator such that turbulence properties are optimized at the combustor-turbine interface. We modify the size, orientation, and positioning of the primary and dilution jets to minimize turbulence intensity at the combustor exit while demonstrating negligible or favorable changes to the pressure loss and mixing characteristics of the combustor. The optimization is performed using a machine learning surrogate-assisted genetic algorithm coupled with large eddy simulations (LES) and Reynolds-averaged Navier Stokes (RANS) simulations. The optimization is performed in three phases: (i) we develop a continuously-learning artificial neural network surrogate model, (ii) we perform a stochastic optimization with RANS simulations to narrow the parameter space, and (iii) we perform a stochastic optimization with a coarse-grid LES to identify the optimal solution. Using this approach, we are able to achieve a 5.35% reduction in turbulence intensity and a 0.42% reduction in pressure loss while maintaining good mixing uniformity at the combustor exit. These changes are enabled primarily by changing the aspect ratio and diameter of the primary zone and dilution jets, as well as the chute height and spacing of the primary zone jets. This successful demonstration of multi-fidelity optimization in the combustor simulator can be extended in the future to the design of improved gas turbine combustors.