As power demand is increased, power generation and especially distributed generation (DG) are being developed. Therefore, power distribution systems become increasingly complicated and short circuit level in distribution grids is being augmented. Thereby, installation of a superconducting fault current limiter (SFCL) is a logical solution to decrease the fault current level in a distribution network. Preventing distribution system degradation by high fault currents, lower equipment ratings, and economic issues are the advantages of SFCL in distribution grids. However, SFCL installation causes delayed operation of the existing overcurrent protection and requires recoordination of the relays. In addition, disconnecting the SFCL from the distribution circuit due to maintenance leads to miscoordination between the overcurrent relays. In this research work, a genetic algorithm (GA) is used to achieve optimal protection coordination in the presence of both SFCL and DG. Furthermore, the uncertainty associated with the connection status of SFCL and DGs, which are reflected in the protection coordination, is investigated in detail. Moreover, various overcurrent relay characteristics, such as long-time inverse, extremely inverse, very inverse, and normally inverse, are used in a test power system, and remarkable computation results will be shown and discussed in the next parts of the paper.