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Fast restoration of critical loads and non-black-start generators can significantly reduce the economic losses caused by power system blackouts. In a parallel power system restoration scenario, the sectionalization of restoration subsystems plays a very important role in determining the pickup of critical loads before synchronization. Most existing research mainly focuses on the startup of non-black-start generators. The restoration of critical loads, especially the loads with cold load characteristics, has not yet been addressed in optimizing the subsystem divisions. As a result, sectionalized restoration subsystems cannot achieve the best coordination between the pickup of loads and the ramping of generators. In order to generate sectionalizing strategies considering the pickup of critical loads in parallel power system restoration scenarios, an optimization model considering power system constraints, the characteristics of the cold load pickup and the features of generator startup is proposed in this paper. A bi-level programming approach is employed to solve the proposed sectionalizing model. In the upper level the optimal sectionalizing problem for the restoration subsystems is addressed, while in the lower level the objective is to minimize the outage durations of critical loads. The proposed sectionalizing model has been validated by the New-England 39-bus system and the IEEE 118-bus system. Further comparisons with some existing methods are carried out as well. [ABSTRACT FROM AUTHOR]