Due to the topological structure of double columns and multiple separating sections in dividing-wall distillation columns (DWDCs), the development of vapor recompressed dividing-wall distillation columns (DWDC-VRHPs) represents a challenging issue with great complexities and tediousness. For the separations of light-component dominated and wide boiling-point tary mixtures, because the purification of the light-component from the intermediate- and heavy-components incurs the primary energy dissipation, the application of vapor recompressed heat pumps (VRHP) should be aimed to reduce the irreversibility and this leads to the generation of the optimum topological structures of the DWDC-VRHPs, i.e., a DWDC plus a two-stage VRHP. The first-stage VRHP is to preheat feed, not only taking the advantages of the small temperature elevation available but also fa-voring the mass transfer between the vapor and liquid phases through feed splitting. The second-stage VRHP is to reduce further separation irreversibility. The philosophy can be applied to any DWDCs no matter where the di-viding wall locates. Two case studies on the separations of tary mixtures of benzene, toluene, and o-xylene and n-pentane, n-hexane, and n-heptane demonstrate the economic optimality of the proposed DWDC-VRHPs and reveal the inherent interplay between intal and extal process integration.