This paper presents a genetic algorithm (GA) method for determining the lowest energy structure of atomic clusters in arbitrary model potentials. The method outperforms simulated annealing, as demonstrated by its efficient finding of fullerene structures up to C60 from random coordinates. The GA operates on a population of candidate structures, selecting parents based on their energy and producing offspring through mating. The algorithm is efficient in finding the ground state of clusters, even with strong directional bonds that create large energy barriers. The GA is applied to optimize the geometry of carbon clusters up to C60, successfully finding the ground state structures from random coordinates. The method involves mating two parent geometries by cutting them along a plane and assembling the child from atoms above and below the plane. The algorithm also includes mutation to explore alternative structural classes, which is essential for finding the global minimum in complex energy landscapes. The paper discusses the application of the GA to carbon clusters, showing that it can reliably find the correct structure even when simulated annealing fails. The GA is compared to simulated annealing, with the GA showing greater efficiency in finding the global minimum. The method is also applied to other systems, indicating its broad applicability in structural optimization. The paper highlights the advantages of the GA over simulated annealing, particularly in handling complex energy landscapes and large clusters. The GA's ability to efficiently explore the phase space and find the global minimum makes it a promising tool for molecular geometry optimization. The study also discusses the importance of mutation in the GA, which allows the algorithm to escape local minima and explore alternative structures. The results show that the GA is effective in finding the correct structures for carbon clusters, even when other methods fail. The paper concludes that the GA is a powerful tool for molecular geometry optimization, with potential applications in various fields of chemistry and materials science.This paper presents a genetic algorithm (GA) method for determining the lowest energy structure of atomic clusters in arbitrary model potentials. The method outperforms simulated annealing, as demonstrated by its efficient finding of fullerene structures up to C60 from random coordinates. The GA operates on a population of candidate structures, selecting parents based on their energy and producing offspring through mating. The algorithm is efficient in finding the ground state of clusters, even with strong directional bonds that create large energy barriers. The GA is applied to optimize the geometry of carbon clusters up to C60, successfully finding the ground state structures from random coordinates. The method involves mating two parent geometries by cutting them along a plane and assembling the child from atoms above and below the plane. The algorithm also includes mutation to explore alternative structural classes, which is essential for finding the global minimum in complex energy landscapes. The paper discusses the application of the GA to carbon clusters, showing that it can reliably find the correct structure even when simulated annealing fails. The GA is compared to simulated annealing, with the GA showing greater efficiency in finding the global minimum. The method is also applied to other systems, indicating its broad applicability in structural optimization. The paper highlights the advantages of the GA over simulated annealing, particularly in handling complex energy landscapes and large clusters. The GA's ability to efficiently explore the phase space and find the global minimum makes it a promising tool for molecular geometry optimization. The study also discusses the importance of mutation in the GA, which allows the algorithm to escape local minima and explore alternative structures. The results show that the GA is effective in finding the correct structures for carbon clusters, even when other methods fail. The paper concludes that the GA is a powerful tool for molecular geometry optimization, with potential applications in various fields of chemistry and materials science.