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This open access book introduces external factors such as loads and constraints into the theory of configurational vulnerability, thereby overcoming the classical theory's inability to account for external influences. Stability is a governing factor in the design of single-layer gridshells, becoming increasingly critical as the span grows. However, current design methodologies address stability primarily through post-design verification, which severs the intrinsic link between member design and overall structural stability. This disjointed approach leads to iterative cycles of design and verification, reducing efficiency. Concurrently, advances in industrialized construction have spurred the development of numerous innovative joints tailored for prefabricated construction. These joints are neither ideally rigid nor ideally hinged. Yet, prevailing design methods and stability verification processes still assume ideal rigid connections, failing to incorporate the mechanical properties of joints and thereby constraining the adoption and application of these new designs. This integration provides a novel perspective on instability mechanisms. Based on the instability mechanisms of gridshells, a stability optimization model is developed under the rigid joint assumption. Due to the large number of variables involved in the optimization model, conventional algorithms often prove inadequate. To address this, the study enhances the standard genetic algorithm by replacing its random mutation mechanism with a directed mutation mechanism, significantly improving search efficiency. The improved algorithm efficiently solves large-scale stability optimization problems for single-layer gridshells, as validated using three gridshells of varying scales and two constructed examples. To expand the forms of gridshell joints, the study employs advanced topology optimization techniques to enhance rotational stiffness. Simultaneously, the study integrates the requirements of prefabricated construction by designing a universal connection interface capable of accommodating members from diverse orientations. This effort culminates in the development of novel joint designs for spatial grid structures that are both mechanically efficient and construction-friendly.