In this paper, following a description-driven paradigm, we aim to establish a generalized governing equation (GGE) for structural optimization. Within this paradigm, the description—representing the material distribution—is generated using two arbitrarily defined high-dimensional hypersurfaces, while the drive—characterized by sensitivity measures such as elemental sensitivity, shape derivatives, and topological derivatives—guides the evolution of the material distribution. The proposed GGE integrates both elements, transforming material optimization into the evolution of these two surrogate hypersurfaces. The generalized evolution of the hypersurfaces is further decomposed into tangential and orthogonal components. In the tangential directions, the GGE enables shape modifications, whereas in the orthogonal direction, it facilitates topological changes. Through this dual evolution process, the GGE unifies shape and topology optimization within a single framework. Numerical examples demonstrate the effectiveness and efficiency of this approach. The establishment of the GGE is significant in bridging the gaps among various structural optimization methods, fostering a deeper understanding of diverse optimization strategies.