The wake effect is a relevant factor in determining the optimal distribution of wind turbines within the boundaries of a wind farm. This reduces the incident wind speed on downstream wind turbines, which results in a decrease in energy production for the wind farm. This paper proposes a novel approach for optimizing the distribution of wind turbines using a new Genetic Gray Wolf Optimizer (GGWO). The GGWO employs a teamwork model inspired by wolf prey hunting, guided by four leaders: Alpha, Beta, Delta, and Omicron wolves, each with different hierarchical weights. To improve the competitiveness of the wolves, GGWO utilizes genetic algorithm operators such as crossover blending, normal mutation, and a new genetic operator called Random Selective Mutation (RSM), which improves solution search efficiency. The proposed GGWO is compared to other algorithms such as Gray Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Ant Colony Optimization (ACO). The studies examine varying wind speeds in magnitude and direction throughout the year, as well as different wind farm boundaries. The outcomes show that GGWO successfully identifies the ideal locations for wind turbines, scoring better scores in terms of total simulation duration and annual energy generation for the wind farm. It surpasses the performance of GWO, ABC, and PSO algorithms and exhibits comparable competitiveness with more intricate algorithms like ACO.