In the context of simulation-based design optimization, the number of simulations necessary to converge to an optimal design often dictates the efficacy of the optimization process. Efficient gradient-based optimization algorithms require information regarding the sensitivity of the objective function with respect to the design variables. However, acquiring this information can be challenging without major modification of the simulation code or inefficient approximations. The employment of a surrogate model decouples the optimization from the simulations enabling derivative-free optimization. In the context of simulation-based optimization of hydrogen burners, the mixing process of fuel and oxidizer inside the burners can be simulated and optimized. This can be realized with different turbulence modeling approaches with varying levels of fidelity. To efficiently optimize the burner’s internal geometry, multi-fidelity optimization is employed, leveraging the strengths of each turbulence modeling approach. This is realized by using a surrogate model that takes different fidelity levels into account. The construction of the surrogate model involves sampling of the design space according to approach from the field of Design of Experiments. As the simulations corresponding to the sampled points are independent from each other, multiple simulations can be executed simultaneously. Since no communication between the simulations is required during execution, this method exhibits excellent scaling behavior on HPC systems.