Solvent-based separation processes, such as extractive distillation, show large potential for the separation of azeotropic mixtures. However, these processes are rather complex to design and optimize since the overall process performance depends strongly on the choice and amount of solvent and can only be evaluated for a process flowsheet with closed recycles. It is important to note that the potential for heat integration also depends strongly on the solvent choice. Consequently, a successive selection of a suitable solvent followed by process design and optimization and finally energy integration likely results in suboptimal choices. In order to allow for direct optimization of an extractive distillation process, including solvent selection and different means for energy integration, the current study proposes the use of a hybrid evolutionary-deterministic algorithm. The application is demonstrated for the separation of an azeotropic acetone-methanol mixture, considering six solvent candidates and up to four alternative means for energy integration. The results illustrate the existence of a multitude of suboptimal local solutions and demonstrate the capability of the proposed method to effectively overcome these limitations.