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This paper proposes a new strategy for solving the service restoration problem in large-scale distribution systems (DS). Due to the presence of various conflicting objective functions and constraints, the service restoration task is a multi-objective, multi-constraint optimization problem. As a consequence, finding feasible solutions is a hard task. The proposed strategy uses a new tree encoding, called node-depth encoding (NDE), and a modified version of the non-dominated sorting genetic algorithm-II (NSGA-II). Using NDE and its operators the proposed strategy generates only radial configurations without disconnected areas reducing the running time necessary to find feasible solutions. On the other hand, the use of the modified version of the NSGA-II enables an efficient exploration of the search space. The efficiency of the proposed strategy is shown using a Brazilian DS, with 3,860 buses, 635 switches, 3 substations, 23 feeders, 2 transformers of 50 MVA and 1 transformer of 25 MVA.