The paper presents a method for determining the lowest energy structure of atomic clusters using a genetic algorithm (GA). The GA operates on a population of candidate structures, evolving them to produce new candidates with lower energies. This method outperforms simulated annealing, as demonstrated through its application to a tight-binding model potential for carbon clusters. The algorithm efficiently finds the ground state structures of fullerene clusters up to C$_{60}$, starting from random atomic coordinates. The authors describe the details of their GA procedure, including the mating operator, relaxation techniques, and mutation operators. They show that the GA can reliably find the correct structures, even in cases with multiple competing low-energy states, by allowing searches for alternate structural classes through mutation. The efficiency of the GA is highlighted, particularly in larger clusters, and the authors suggest that further improvements can be achieved by assuming the class of desired structures and using a more complex mapping between the genetic representation and the cluster structure.The paper presents a method for determining the lowest energy structure of atomic clusters using a genetic algorithm (GA). The GA operates on a population of candidate structures, evolving them to produce new candidates with lower energies. This method outperforms simulated annealing, as demonstrated through its application to a tight-binding model potential for carbon clusters. The algorithm efficiently finds the ground state structures of fullerene clusters up to C$_{60}$, starting from random atomic coordinates. The authors describe the details of their GA procedure, including the mating operator, relaxation techniques, and mutation operators. They show that the GA can reliably find the correct structures, even in cases with multiple competing low-energy states, by allowing searches for alternate structural classes through mutation. The efficiency of the GA is highlighted, particularly in larger clusters, and the authors suggest that further improvements can be achieved by assuming the class of desired structures and using a more complex mapping between the genetic representation and the cluster structure.