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Genetic algorithm (GA) has shown its promise in dealing with reliability evaluation of complex power systems. However, it may be computationally expensive due to its stochastic search mechanism coupled with the problem complexity. Especially, when each system state needs a load flow calculation to determine its status, the reliability evaluation process may take a long time. Parallel computation is being more widely used because of the increasing computing capability. In this paper, the parallel computation mechanism is incorporated into the GA in order to increase its computational efficiency. Several parallel computation topologies are introduced, and conceptual comparisons with respect to parallel Monte Carlo simulation are detailed. Also some preliminary numerical studies are carried out to examine their performance in terms of computing cost and solution quality.