Exoskeletons can boost human strength and provide assistance to individuals with physical disabilities. However, ensuring safety and optimal performance in their design poses substantial challenges. This study presents the design process for an underactuated hand exoskeleton (U-HEx), first including a single objective (maximizing force transmission), then expanding into multi objective (also minimizing torque variance and actuator displacement). The optimization relies on a Genetic Algorithm, the Big Bang-Big Crunch Algorithm, and their versions for multi-objective optimization. Analyses revealed that using Big Bang-Big Crunch provides high and more consistent results in terms of optimality with lower convergence time. In addition, adding more objectives offers a variety of trade-off solutions to the designers, who might later set priorities for the objectives without repeating the process - at the cost of complicating the optimization algorithm and computational burden. These findings underline the importance of performing proper optimization while designing exoskeletons, as well as providing a significant improvement to this specific robotic design.