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Energy system integration enables raising operational synergies by coupling the energy infrastructures for electricity, methane, and hydrogen. However, this coupling reinforces the infrastructure interdependencies, increasing the need for integrated modeling of these infrastructures. To analyze the cost-efficient, sustainable, and secure dispatch of applied, large-scale energy infrastructures, an extensive and non-linear optimization problem needs to be solved. This paper introduces a nested decomposition approach with three stages. The method enables an integrated and full-year consideration of large-scale multi-energy systems in hourly resolution, taking into account physical laws of power flows in electricity and gas transmission systems as boundary conditions. For this purpose, a zooming technique successively reduces the temporal scope while first increasing the spatial and last the technical resolution. A use case proves the applicability of the presented approach to large-scale energy systems. To this end, the model is applied to an integrated European energy system model with a detailed focus on Germany in a challenging transport situation. The use case demonstrates the temporal, regional, and cross-sectoral interdependencies in the dispatch of integrated energy infrastructures and thus the benefits of the introduced approach. [ABSTRACT FROM AUTHOR]