As modern computational and modeling technologies grow, engineering design heavily relies on computer modeling and simulation to accelerate design cycles and save cost. A complex design problem will involve many design parameters and tables. Exploring design space and finding optimal solutions are still major challenges for complex systems. This dissertation proposed to use Genetic Algorithms to optimize engineering design problems. It proposed a software infrastructure to combine engineering modeling with Genetic algorithms and covered several aspects in engineering design problems. The dissertation suggested a new Genetic Algorithm (Completely dominant Genetic algorithm) to quickly identify High Performance Areas for Engineering Design. To help design engineers to explore design space, the dissertation used a new visualization tool to demonstrate high dimensional Genetic Algorithm results in dynamical graphics. Robustness of design is critical for some of the engineering design applications due to perturbation and manufacturing tolerance. This dissertation demonstrated to use Genetic Algorithms to locate robust design areas and provided a thorough discussion on robustness and diversity in depth.