In early-stage architectural design, optimization algorithms are essential for efficiently exploring large and complex design spaces under tight computational constraints. While prior research has benchmarked various optimization methods, their findings often lack generalizability to real-world, domain-specific problems, particularly in early building design optimization for energy performance. This study evaluates the effectiveness of Genetic Algorithms (GAs) for early design optimization, focusing on their ability to find near-optimal solutions within limited timeframes. Using a constrained case study, we compare a simple GA to two baseline methods, Random Search (RS) and Grid Search (GS), with each algorithm tested 10 times to enhance the reliability of the conclusions. Our findings show that while RS may miss optimal solutions due to its stochastic nature, it was unexpectedly effective under tight computational limits. Despite being more systematic, GS was outperformed by RS, likely due to the irregular design search space. This suggests that, under strict computational constraints, lightweight methods like RS can sometimes outperform more complex approaches like GA. As this study is limited to a single case under specific constraints, future research should investigate a broader range of design scenarios and computational settings to validate and generalize the findings. Additionally, the potential of Random Search or hybrid optimization methods should be further investigated, particularly in contexts with strict computational limitations.