Robotic exoskeletons can enhance human strength and aid people with physical disabilities. However, designing them to ensure safety and optimal performance presents significant challenges. Developing exoskeletons should incorporate specific optimization algorithms to find the best design. This study investigates the potential of Evolutionary Computation (EC) methods in robotic design optimization, with an underactuated hand exoskeleton (U-HEx) used as a case study. We propose improving the performance and usability of the U-HEx design, which was initially optimized using a naive brute-force approach, by integrating EC techniques such as Genetic Algorithm and Big Bang-Big Crunch Algorithm. Comparative analysis revealed that EC methods consistently yield more precise and optimal solutions than brute force in a significantly shorter time. This allowed us to improve the optimization by increasing the number of variables in the design, which was impossible with naive methods. The results show significant improvements in terms of the torque magnitude the device transfers to the user, enhancing its efficiency. These findings underline the importance of performing proper optimization while designing exoskeletons, as well as providing a significant improvement to this specific robotic design.