The restoration process of a power system after a blackout consists of three phases, namely starting up the generators, re-energizing the network, and picking the loads. The generator start-up sequence is pivotal for the total restoration time and the following restoration steps. In this paper, a novel algorithm for optimizing a generator start-up sequence is proposed. Based on the VIKOR method, which is a multiobjective approach, the proposed algorithm is not only able to improve the start-up time and reliability of a generator start-up sequence, but can also handle auxiliary optimization criteria with priorities that change during the start-up. Such criteria are, for instance, the importance of the power increasing rate, reliability and surrounding topologies of generators. The efficiency of the proposed method is evaluated in two tests. In the first test exhaustive search is used to compute optimal solutions. In the second and larger test NSGA-II is utilized to approximate the Pareto frontier. For both tests the proposed algorithm approximates the reference results while being computationally very efficient. This makes it suitable for online decision making where a new startup sequence has to be computed in a few seconds or minutes.