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• A novel generator start-up sequence optimization strategy is proposed in this work, taking the integration time of wind-solar hybrid systems into account. • The proposed model requires fewer variables compared with other models, therefore the computational efficiency can be greatly improved. • The confidence gap decision theory based generator start-up sequence strategy is proposed to address the generation uncertainty of wind-solar hybrid systems. • Better generator start-up sequence solutions with higher computational efficiency and less conservatism can be attained by employing the proposed strategy. A reasonable start-up sequence of generators considering renewable energy generation integration can effectively improve the restoration efficiency of the power system concerned. The restoration strategy of generators is time-sensitive, however, the computation procedure of existing methods is not fast enough to meet the requirements of practical applications. In this paper, the generator start-up sequence optimization (GSSO) problem is addressed with the integration of wind-solar hybrid systems (WSSs) considered in bulk power systems. Specifically, a deterministic model for GSSO is formulated to maximize the total generation capability during the restoration procedure, in which fewer auxiliary variables are required to promote the computational efficiency. On this basis, in order to deal with the inherent and significant uncertainties of WSSs, a confidence gap decision theory (CGDT) based approach is proposed combining the advantages of stochastic optimization and the information gap decision theory based method while considering the worst-case realization of unknown probability distributions, so that a chance-constrained robust generator start-up solution is thereby attained. Moreover, the formulated CGDT based model is transformed into a mixed integer linear programming problem. Finally, the IEEE 39-bus power system and a modified version of an actual power system in China are employed to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]