Approximation Algorithms for the Minimum Number of Matches Problem in Heat Exchanger Network Synthesis

Abstract

Although the use of heuristics has been prevalent in the process synthesis literature, their justification has been exclusively based on empirical evidence obtained through computational testing. As a result, heuristics currently in use offer no guarantee of optimality. Optimization algorithms, on the other hand, offer rigor but suffer from the combinatorial explosion of computational requirements necessary to produce an optimal solution. Recognizing this gap between heuristic and optimization approaches in process synthesis, we propose the use of analytical techniques in the development and assessment of heuristics. The primary purpose of this paper is to introduce the analysis of algorithm performance into the field of process synthesis and develop the first approximation algorithms for process synthesis. Approximation algorithms are heuristics with guaranteed performance. In the context of the classical matches problem in heat exchanger network synthesis, we develop approximation algorithms based on primal rounding, dual rounding, Lagrangean relaxation rounding, primal−dual approximation, and greedy approximation. We provide an analytical characterization of the worst-case behavior of these as well as any heuristic that may be devised for the matches problem. In computational experiments with a test set of 29 problems from the literature, we find that the developed suite of algorithms performs much better than its theoretical worst-case bound and provides solutions that average within 25% of optimality. On the other hand, five of these test problems are beyond the capabilities of current state-of-the-art optimization software. Finally, we pose a number of interesting research challenges in this area.

A perspective on process synthesis: Challenges and prospects

“…However, the author refers the interested reader to a selected subset of excellent reviews and perspective papers on: reactor and reactor-separator network synthesis focusing on attainable region construction (Feinberg, 2002), synthesis of heat integration networks (Furman and Sahinidis, 2004;Morar and Agachi, 2010), water network synthesis (Jez˙ owski, 2010), distillation-based separation sequence synthesis (Skiborowski et al, 2013), and general process synthesis approaches focusing on their substantial potential for synthesis of sustainable and environmentally-friendly processes for energy and chemicals production (Grossmann and Guillén-Gosálbez, 2010;Yuan and Chen, 2012;Yuan et al, 2013).…”

Globally optimal synthesis of heat exchanger networks. Part I: Minimal networks

“…Such definition almost always leads to a total number of units that is larger than N min (as defined above), and consequently these structures are rarely MSTR structures. Similarly, structures with nonisothermal mixing and with bypasses that cannot be represented by the staged superstructure have been studied and rendered values given by N min that are virtually impossible using other limited superstructures.Remark There have been several studies in the literature regarding the a‐priori calculation of the minimum number of units, sometimes referred to as minimum number of matches . Letsios et al presented a proof that the minimum number is N min = NH + NC + NHU + NCU‐L , where NHU and NCU are the number of hot and cold utilities types respectively and L ∈ [1, Min { NH + NHU , NC + NCU }].…”

Approximation algorithms for process systems engineering

“…Continuous variables t H i,j,k and t C i,j,k express the exiting temperature of hot stream Figure 5: In the transportation model (Cerda and Westerburg, 1983), each hot stream i supplies σ i,t units of heat in temperature interval t which can be received, in the same or a lower temperature interval, by a cold stream j which demands δ j,t units of heat in t. In the transshipment model (Papoulias and Grossmann, 1983), there are also intermediate nodes transferring residual heat to a lower temperature interval. This figure is adapted from Furman and Sahinidis (2004).…”