The electrical system of a nuclear reactor facility (NRF) must incorporate a grounding grid in order to ensure it functions safely and reliably. Any disturbance in the electrical system affects the nuclear process, so it is, therefore, crucial to estimate the safety performance of the research nuclear reactor facility grounding system. The paper discusses CYMGrd 6.3, which is based on IEEE Standard 80-2013, and the optimization approaches for finding the best grounding grid design for a nuclear reactor facility connected substation of 500/11 kV in the case of a ground fault and lightning strikes. The result shows that the surface, step and touch potentials along the diagonal coordinates of the proposed grounding grid are below the safety limits in case of a ground fault but also results indicate that 100 kA lightning stroke poses a considerable threat to reactor equipment and personnel safety because the measured grid surface potential exceeds the safe ground potential rise of 3.2 kV standard at the striking point in conjunction with the proposed ground grid, so it must be modified. In this paper, three different optimization algorithms are investigated in order to determine the optimal design of the grounding grid with respect to mesh size: gradient method (GM), the genetic algorithm (GA), and simulated annealing (SA). These methods are used to achieve the purpose of obtaining an effective ground grid design. Comparing these techniques of GM and SA is good for quickly locating local minima, but they may fail to identify global solutions. In contrast, a genetic algorithm is often excellent at achieving a global minimum. Also, the utilization of GA, SA, and GM achieve the reduction of the surface potential of a proposed grounding grid by 16 %, 10 %, and 6 % respectively.