Computational design can excite the full potential of soft robotics that has the drawbacks of being highly nonlinear from material, structure, and contact. Up to date, enthusiastic research interests have been demonstrated for individual soft fingers, but the frame design space (how each soft finger is assembled) remains largely unexplored. Computationally design remains challenging for the finger-based soft gripper to grip across multiple geometrical-distinct object types successfully. Including the design space for the gripper frame can bring huge difficulties for conventional optimisation algorithms and fitness calculation methods due to the exponential growth of high-dimensional design space. This work proposes an automated computational design optimisation framework that generates gripper diversity to individually grasp geometrically distinct object types based on a quality-diversity approach. This work first discusses a significantly large design space (28 design parameters) for a finger-based soft gripper, including the rarely-explored design space of finger arrangement that is converted to various configurations to arrange individual soft fingers. Then, a contact-based Finite Element Modelling (FEM) is proposed in SOFA to output high-fidelity grasping data for fitness evaluation and feature measurements. Finally, diverse gripper designs are obtained from the framework while considering features such as the volume and workspace of grippers. This work bridges the gap of computationally exploring the vast design space of finger-based soft grippers while grasping large geometrically distinct object types with a simple control scheme.