Well control optimization in petroleum reservoir management problems is notoriously complex. In general, it requires a large number of computationally expensive simulations, which poses challenges for its practical application. This work presents a variable-fidelity surrogate model strategy for the robust optimization of well control, considering multiple reservoir realizations under geological uncertainties. The method combines wavelet-based local refinement with grid upscaling procedures to construct surrogate models within a hierarchical trust-region optimization framework [1]. The proposed approach features three levels of fidelity. In the initial stage, low-fidelity samples are used to build the surrogate model, representing the basic trend of the objective function and guiding the optimizer during the exploration phase. In the intermediate and final stages, higher-fidelity models are progressively used to construct new surrogate models, increasing prediction accuracy. This allows for a balance between computational cost and the precision required at each stage of the optimization. The extension to cases involving geological uncertainties considers multiple equiprobable reservoir realizations, where the optimization seeks to maximize a robust metric representing the expected performance under uncertainty. The variable-fidelity strategy is applied simultaneously to a subset of realizations, exploiting the capacity of low-fidelity models to capture overall objective function trends under uncertainties, while high-fidelity models refine estimates in the most promising regions of the decision space [2]. Results are presented for the literature benchmark UNISIM-I-M, considering 48 realizations with different petrophysical property distributions. The methodology reduced computational costs by approximately 80% compared to traditional high-fidelity surrogate-based optimization while maintaining accuracy, even in the context of multiple geological realizations.