The design of optimal Low Earth Orbit (LEO) constellations is a complex, high-dimensional challenge central to modern telecommunications. While Genetic Algorithms (GAs) are potent optimization tools, their performance is notoriously sensitive to initial parameter settings, often leading to premature convergence and suboptimal designs. This paper introduces a novel Fully Adaptive Genetic Algorithm (AGA), engineered to overcome this critical limitation through a dynamic, self-correcting framework. The AGA employs an external control loop that co adjusts population size and crossover fraction based on real-time metrics of population diversity and convergence stagnation. To rigorously test its resilience, the AGA was intentionally initialized with the worst-performing parameters from a static GA baseline a configuration guaranteed to fail.First, its robustness was validated on the high-dimensional Rastrigin benchmark function, where, despite the poor start, it outperformed the best static GA by an astonishing factor of 380, proving its exceptional ability to escape deep local optima. The validated AGA was then applied to its primary mission: optimizing a 10-satellite, 30 variable LEO constellation for maximal coverage over Tehran. The results were decisive. The AGA achieved 19.45 hours of daily coverage, a 14.4% improvement over the 17.00 hours achieved by the best-tuned static GA. More remarkably, it accomplished this in just 15 hours, an 80.8% reduction from the 78 hours required by the static GA. This research not only contributes a highly efficient and reliable methodology for indigenous satellite constellation design but also presents a powerful paradigm for solving complex engineering problems where parameter sensitivity is major bottleneck