*3.2. Structural Feasibility Assessment—Reduction of Superstructure*

In the next step, the structural feasibility of the identified proposals is analyzed. As outlined in Section 2.1, this can be done by calculating the flexibility index discarding all design constraints and considering only structural constraints. The flexibility index can be calculated using the active set approach developed by Floudas and Grossman [39]. However, the active set approach may result in impractical large problem formulations as industrial applications are often complex. Alternative formulations exist, such as the calculation of the flexibility index via the direction matrix [40] or via cylindrical algebraic decomposition and quantifier elimination [41]. However, the first alternative relies on the simulated annealing algorithm, which means that the global solution may not be found in a reasonable period of time. Moreover, applying cylindrical decomposition to industrial applications (which typically involve more than four HEXs and uncertain parameters) requires excessive computational capacity, which may not be available. An alternative is Monte Carlo network simulations with random variations within the uncertainty span while degrees of freedom are utilized to control operational targets and minimize utility cost in a similar way as it was proposed by Kachacha et al. in [46]. With an increasing number of uncertain parameters and complexity of the problem, computational capacity is the limiting factor for this approach. Although all listed methodologies for (structural) feasibility assessment have known drawbacks, it is assumed that structural feasibility assessment of HENs (also in more complex industrial applications) is possible. To reduce the probability of faulty results, the authors suggest applying several of the proposed methods and compare the achieved results. If design proposals can be identified that are structurally infeasible for at least some operating points within the uncertainty span (i.e., flexibility index smaller than 1), these design proposals are excluded from the superstructure, yielding a reduced superstructure.

**Figure 2.** Retrofitting framework to achieve flexible and cost-efficient retrofit measures of heat exchanger networks (HENs).
