Distillation-based separation processes, such as extractive or heteroazeotropic distillation, present important processes for separating azeotropic mixtures in the chemical and biochemical industry. However, heteroazeotropic distillation has received much less attention than extractive distillation, which can be attributed to multiple reasons. The phase equilibrium calculations require a correct evaluation of phase stability, while the topology of the heterogeneous mixtures is generally more complex, comprising multiple azeotropes and distillation regions, resulting in an increased modeling complexity. Due to the integration of distillation columns and a decanter, even the simulation of these processes is considered more challenging, while an optimal process design should include the selection of a suitable solvent, considering the performance of the integrated hybrid process. Yet, the intricate mixture topologies largely impede the use of simplified criteria for solvent selection. To overcome these limitations and allow for a process-based screening of potential solvents, the current work presents a topology-based initialization and optimization approach for designing heteroazeotropic distillation processes. The systematic initialization enables an efficient evaluation of different solvents with different mixture topologies, which is further exploited for optimization-based sensitivity analysis and multi-objective optimization. Three case studies are analyzed with about 170 individually optimized process designs, including stage numbers, feed locations, phase ratios, and heat duties.