Neural Architecture Search (NAS) methods, which aim to identify the best architecture for a given problem, have demonstrated their effectiveness across various domains, from computer vision to natural language processing. These approaches have significantly contributed to optimizing performance while addressing constraints such as computational efficiency and resource management. The Genetic Neural Architecture Search (GeNAS) proposed in this work illustrates the potential of NAS to go beyond its traditional objective of finding optimal architectures. While NAS is often employed to address constraints such as memory management and latency reduction, our study focuses on the critical challenge of minimizing False Negatives, with the ultimate goal of achieving Zero False Negatives (ZFN). To address this challenge, we integrate a methodology based on the Augmented Lagrangian Method (ALM), allowing for a better consideration of specific problem constraints. By adopting this targeted strategy, GeNAS demonstrates its effectiveness in tackling critical problems that require both high performance and enhanced sensitivity.