Distillation accounts for a large percentage of the energy used in the manufacturing industry. As energy costs rise, hybrid separation strategies-strategies that combine one or more separation techniques with distillations are attracting attention as a means of saving energy. Examples of hybrid separation schemes include extraction followed by distillation, reactive distillation, adsorption/distillation, and others. In this work, the energy efficiency of hybrid separation schemes is studied using the novel concept of shortest separation lines. Hybrid separation of acetic acid and water using extraction/distillation is used to show that the shortest separation lines correctly define the target extract compositions for the extractor and lead to the most energy efficient hybrid separations. A global optimization strategy, which uses a mixture of feasible and infeasible subsets of constraints to avoid the discrete nature of the feasible region, is presented for directly computing the most energy efficient hybrid separation schemes.