**4. Conclusions**

The presented approach to incorporate a flexible cost functions framework to synthesize cost-optimal heat exchanger networks (HENs) was carried out successfully and showed promising results. The flexible structured objective function allows for the integration of individual, match-dependent cost functions. The introduction of pseudo streams in combination with the flexible cost functions framework allow for the application for various problems. Corresponding optimizations utilizing different parametrizations have been carried out successfully. The universal applicability was shown by the execution of optimizations with different areas of application. The presented approach is applicable for direct as well as indirect heat integration utilizing the same superstructure and the same genetic algorithm for solving the problems. The use for combined direct and indirect heat integration is possible if initially forbidden matches ge<sup>t</sup> extended with cost information. This work presents results with lower TAC than other results published in literature beforehand.

For the practical implementation it is advisable to incorporate factors like piping already during optimization. The consideration of these factors can have a huge impact of the overall HEN structure and can lead towards significantly different and more efficient solutions. Local clustering was observed for some solutions like already reported by Rathjens and Fieg [1].

**Author Contributions:** Conceptualization, M.R.; methodology, M.R.; software, M.R.; validation, M.R. and G.F.; formal analysis, M.R.; investigation, M.R.; resources, M.R. and G.F.; data curation, M.R.; Writing—Original Draft preparation, M.R.; Writing—Review and Editing, M.R. and G.F.; visualization, M.R.; supervision, G.F.; project administration, M.R. and G.F.; funding acquisition, M.R. and G.F.

**Funding:** Authors would like to acknowledge the financial support from German Federal Ministry for Economic Affairs and Energy through ZIM program (Zentrales Innovationsprogramm Mittelstand, project number: ZF4025905CL7). The publication was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number: 392323616 and the Hamburg University of Technology (TUHH) in the funding program "Open Access Publishing".

**Acknowledgments:** The authors gratefully acknowledge the support of our industrial partner, the "weyer group".

**Conflicts of Interest:** The authors declare no conflict of interest.
