Global Geometry (or Cluster) optimization is the process of finding the most stable formations of a cluster of some atoms. A genetic algorithm was developed to find the global minimum of a cluster using the Lennard-Jones atom interaction model efficiently. Determining the optimal yper-parameters for the algorithm is a computationally intractable task without proper search strategies. Furthermore, during different stages of the algorithms it may be beneficial to change the importance of exploration vs exploitation of the search space. To solve these problems, nine strategies of choosing the algorithm’s mutation rate are presented and benchmarked on the time to find the global optimum. Experimental results show that such strategies can reduce the mean time required to find a global minimum for a given cluster when compared to a constant low mutation rate. However, the results are not statistically significant for all clusters tested. The variance in the results might be caused by the understudied factor of the local optimization the algorithm utilizes. A majority of the algorithm’s runtime is taken up by it, leading to the GA components showing less impact on the results.