Computational strategies for large-scale MILP transshipment models for heat exchanger network synthesis

Abstract

Determining the minimum number of units is an important step in heat exchanger network synthesis (HENS). The MILP transshipment model (Papoulias and Grossmann, 1983) and transportation model (Cerda and Westerberg, 1983b) were developed for this purpose. However, they are computationally expensive when solving for large-scale problems. Several approaches are studied in this paper to enable the fast solution of large-scale MILP transshipment models. Model reformulation techniques are developed for tighter formulations with reduced LP relaxation gaps. Solution strategies are also proposed for improving the efficiency of the branch and bound method. Both approaches aim at finding the exact global optimal solution with reduced solution times. Several approximation approaches are also developed for finding good approximate solutions in relatively short times. Case study results show that the MILP transshipment model can be solved for relatively large-scale problems in reasonable times by applying the approaches proposed in this paper. • Several approximation approaches are developed for finding near optimal solutions. Key Words• Some relatively large-scale MILP transshipment models are solved in reasonable times by using the approaches proposed in this study.

Evaluation of the Complexity, Controllability and Observability of Heat Exchanger Networks Based on Structural Analysis of Network Representations

“…The well-known benchmark sets of Furman and Sahinidis (2004) [60], [61,62] and Grossmann (2017) [63] were used to study how the proposed measures can be used to evaluate HENs and compare different design methodologies of HENs. The benchmark problems and the applied methods are summarised in Table 3, while the notation of the utilised methods and their objective functions are shown in Table 4.…”

Detecting Symmetry in Designing Heat Exchanger Networks

“…One way symmetry arises is due to the equal weights on each exchanger. Chen et al (2015) suggest prioritising matches in potential heat exchange areas by reweighing the objective coefficients in the formulation of Papoulias and Grossmann (1983), i.e. the formulation used in this manuscript.…”

“…the formulation used in this manuscript. But Chen et al (2015) do not find significant computational advantages in reweighing the coefficients, so we chose to stick with the simpler formulation of Papoulias and Grossmann (1983). The following formulation, illustrated in Figure 2, represents one fixed temperature interval t = t :…”

A Novel Sequential Approach for the Design of Heat Exchanger Networks

“…In the second step, non-linear programming (NLP) optimization model was applied so that flow rates and heat duties were optimized with the objective of area minimization, therefore minimizing total annual costs. Other important sequential approaches include the vertical heat exchange MILP model of Gundersen and Grossmann (1990) where approach temperatures were treated independently for the whole heat recovery project and each heat exchanger; the improved version of those techniques where an NLP model was included to optimize areas (Gundersen et al, 1997); the modification of the minimum units number sub-problem by Anantharaman et al (2010) using physical insights/heuristics; Chen et al (2015) weighted objective function for utility/capital costs and reformulations for MILP transshipment models; the two-step MILP/MINLP method of Nemet et al (2018) which was able to obtain promising results, including a network for a 173streams problem.…”