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• A MCTS-based method for online deciding the generator startup sequence is proposed. • A constraint about the robustness of restoration scheme is proposed. • The restoration scheme can be adjusted online according to the unexpected faults. Generator startup is a critical step for the power system restoration following blackouts. Most strategies for the startup sequence of generators are obtained by offline methods, which probably are ineffective in the real situation: some devices unexpectedly fail to be restarted. To deal with the uncertainties, this paper proposed a novel method for online decision-making of the startup sequence of generators. First, the framework of online decision making is presented. The principles of online decision-making of the generator startup sequence are analyzed. Second, an optimization model for determining the generator startup sequence is developed to maximize the generating capacity. Then, the Monte Carlo tree search algorithm (MCTS) is applied to online decide the generator to be restored in the next step according to the real-time situation. To make it more suitable for system restoration, MCTS is modified: the upper confidence bounds for trees, the default policy, backpropagation, and the final decision making are improved. The restoration paths related to the selected generator are obtained by a graphic theoretic algorithm. Except commonly used constraints on generator startup and the path restoration, this paper considers the hot start of generators to propose a constraint about the robustness of the restoration scheme. Finally, the feasible strategy with the maximum generating capacity is selected online for application. Case studies on the IEEE 39-bus test system and an actual power system in Hebei, China, demonstrated the effectiveness of this method. [ABSTRACT FROM AUTHOR]