This paper investigates how the local optimization method and strategy affect the efficiency of genetic algorithms (GAs) for Lennard-Jones (LJ) clusters. Several ASE-implemented optimizers were considered; however, only BFGS, FIRE, and Conjugate Gradient (CG) proved viable for integration. The optimizers were first benchmarked independently, and then the GA execution was benchmarked using the different optimizers, with the main solution quality metric being the number of times the global minimum (GM) is found. While BFGS produced better results, its timing was the highest and steepest scaling; furthermore, the trade-off could not be mitigated by reducing the maximal number of optimization steps. In contrast, FIRE and CG, when run with a doubled population size, produced superior results both in terms of execution time and final cluster energy. Furthermore, a cluster isomerism-based heuristic for applying selective local optimization halved the GA's execution time at the expense of a reduction in solution quality. Nonetheless, when computational time was equalized through doubling the population size, the heuristic-based GA produced equal or better results. These findings suggest that faster methods and suboptimal optimization choices, when combined with increased population diversity, can outperform more powerful but slower GA configurations.

Finding the lowest-energy structure of a cluster of atoms is an NP-Hard problem with applications in materials science. Genetic Algorithms (GAs) have shown promise in solving this problem due to their ability to explore complex energy landscapes. A critical component of GAs are the mutations, which maintain diversity and helps avoid premature convergence. Despite the existence of various mutation operations for atomic clusters, there is a lack of benchmarking to compare their effectiveness. In this paper, we evaluate the performance of eight mutation operations within a GA framework for optimizing Lennard-Jones clusters. We assess each mutation based on its ability to reach the global minimum (accuracy) and the time required to do so (runtime). Experiments are conducted across population sizes of 8, 15, and 20, with multiple mutation probabilities tested. Results show that the Etching mutation consistently provides the highest accuracy, but at a considerable runtime cost. In contrast, Twist and Random Displacement offer fast convergence with moderate success rates.

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.

Discovery of new materials is essential in a lot if different fields, such as, space exploration, maritime industry and others. To stop new materials undergoing spontaneous reactions or reacting with the environment, they have to stable or at least metastable. That is where Global Geometry Optimization comes in, which tries to find global minimum on its Potential Energy Surface.
But modeling atoms is difficult as there is complex interplay of forces between each atom. A common simplification is to use the Lennard-Jones potential, which treats atoms as 3D points and models their interactions based on distance.
To find global minimum, Genetic Algorithm will be used and this research plans to study multiple different crossover strategies(sphere cut splice, uniform, two point, one point, arithmetical, plane cut splice crossover) and initialization strategies(box, sphere, octahedron initialization) to determine, which is the best for finding minimum for Lennard-Jones clusters. After analyzing results, it is inconclusive, which crossover produces best results, but it is clear that arithmetical produces worst results and octahedron initialization produces best results for clusters with size 10 to 15.