*3.3. Determination of Critical Points*

In the next step, critical operating points for each design proposal are identified using the different strategies for the identification of candidates for critical points and the set covering algorithm introduced by Pintariˇc and Kravanja [44]. The determination of critical operating points has been implemented in a methodology for synthesis of HENs with large numbers of uncertain parameters [45]. However, it has not yet been implemented in a retrofitting framework. The main difference in a retrofitting framework is that besides the investment cost of new HEXs, investment in existing equipment can also be considered, e.g., heat transfer enhancement or an increase of the area of existing HEXs, as well as structural changes, such as resequencing and repiping of existing HEXs. However, structurally, problems (5) and (6) are similar for a HEN synthesis and a HEN retrofitting problem.

It is worth mentioning that for the critical point analysis, each design proposal (which is present in the reduced superstructure) is considered individually, i.e., for each design proposal, this step yields an individual set of critical points. To allow a fast evaluation of the different design proposals, the different strategies for the identification of candidates for critical points and the set covering algorithm proposed in [44] were automated in this work in order to be applicable to a superstructure-based approach and industrial applications (see Supplementary Material).
