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.