Robot-mounted grippers are used to position, immobilize, and manipulate parts and assemblies during manufacturing. In the design of these systems, the gripper assembly, comprising the grippers that grasp the part and the frame that holds them together, is customized to each part. Due to the large number of design variables and unique design needs for each gripper, automation of gripper assemblies has been limited, especially where multiple gripper types are used to grasp a part. To this end, this article presents an evolutionary approach that synthesizes and optimizes grasps and gripper assembly layouts using two different gripper types—suction cups and magnets—from the geometric models of sheet metal parts. The method first generates an option space of gripper placement on the suitable faces of the part model. Then, a genetic algorithm generates grasps on this option space by varying both the count and locations of each gripper type. Through generations, these grasps are optimized against five criteria and one constraint: factor of safety, cost, residual moment, deflection, frame weight, and gripper clearance. These criteria are then combined into a single criterion that represents a pareto condition for assessing the grasps. The algorithm is implemented in software code for validation, and the article presents detailed validation of the algorithm using four sheet metal parts. The results show that the algorithm improves the grasp from all six aspects, when started from either program-assigned or user-defined initial grasps. The high agreement between the final grasp designs resulting from multiple runs of the algorithm on a part illustrates the stability and repeatability of the algorithm.