In a deregulated electricity market, power system operator should systematically identify the optimal schedule of renewable distributed generation (DG) units to not only optimize the market profits but also improve the network conditions. This paper proposes a parallel computation-based methodology using fuzzy logic designed in the structure of a genetic algorithm (GA). Due to the efficient communication among the processors during the optimization, the proposed fuzzy-based parallel computation GA (FPCGA) addresses the shortcoming of the classic GA in convergence speed and quality of results. The proposed optimization algorithm is utilized in this paper to identify the optimal daily schedule for the system operator including the energy purchased from 1) the power grid, 2) each wind turbine DG, and 3) each photovoltaic DG. The efficiency of the proposed method is verified by its implementation on a 136-bus distribution system and its effectiveness is compared with similar methods.